The answer from @Thomas Markov gives a good explanation of why a check might not be necessary at all - but what if you did need to make a check? Say, if the plan were for you to be taken away by your target and they decide to examine you first?

To answer the more general question of 'how do I make use of my ability in one area if a DM asks me to roll for a different stat' - the simple answer is to just ask the DM.

DM: Okay, you're wild shaped into a goat now, roll a Charisma check to act like a goat.

You: [Oh boy, my Charisma isn't that good...] Could I use my knowledge of Animal Handling instead to behave the way a normal animal would act?

DM: Sure, I'll allow it - roll an Animal Handling check instead.

Just keep in mind that the DM is the final arbiter of what checks you need to make in a given situation - so if he says you can't use Animal Handling to act like a goat (for example, because he views it as an act of controlling animals rather than acting like them), then he has the final say - but it doesn't hurt to ask first.

Behave as the animal

The problem is that, unless you have a vet or someone similar in your group, it may be hard to know, as a player, how do such animals behave, and your opinion on the matter may be different from the opinion of the DM on the matter. Furthermore, it isn't even clear if animals in the world you are playing behave the same way as the animals in our world.

The Monsters Manual presents absolutely no information on the "personality" of most animals, thus, it is entirely up to the DM how each animal would naturally behave in their world. Which leads us to...

Ask your DM

However, your character, the Druid, certainly has that knowledge, and, therefore, you can certainly ask your DM in advance. Your DM may think that a Goat wandering around alone in the middle of nowhere is as suspicious as a goat reading a book or a bear 100 ft under water, and in that case, asking for a roll may be justified (and what roll is the subject of this question). But you can certainly ask if that is the case, and you certainly can ask if there is an animal that would behave like that and still look like an appetizing meal--and your Druid should have that information easily available to them, as it's pretty much their class concept. Maybe a Goat in that world doesn't behave like that, but a Cow or a Moose does.

What I am saying is that the following dialogue is entirely possible:

Druid: So, I want to Wildshape as a goat and act as a bait. In order to do that, I will wander (seemingly) alone in the forest. As a Druid, what do I know about goats behaving like that in this world?

DM: You know that goats are herd animals and no goat that has been raised in a farm would ever be outside the farm, much less in a forest. Anyone seeing a goat in the forest would be suspicious immediately.

Druid: Okay, is there another livestock animal that I could Wildshape as, wander the forest and would be seen like a regular animal?

DM: You remember seeing lots of pigs running around in the forest, and you know that pigs are erratic and often run away from the farms.

Druid: Sure then I will wildshape into a pig!

The pattern here is an even more general advice: be clear on what your expectations are, and try to use the knowledge your character has in order to accomplish such a plan. You, as a player, have no idea on how to do most of the things your character does, so the best you can do is state your intention, and the DM should be the one adjudicating what is the best plan your character can have in order to achieve that goal in that world and helping you out in order to achieve that.

Note, this does not hurt player agency in any way. You can always overrule the DM about what your character thinks, but then your character is probably going to be wrong about that information.

World Building: Players can take part

It is also fairly common (although not the norm) that DMs may allow the players to be part of the world building, so you could ask your DM to let goats in your world to behave like that. I have no idea if that's normal goat-behavior in real life (actually after reading the Wikipedia I kinda do, check below), but I would allow goats in my D&D world to behave like that if a player wanted for some reason that was not game breaking. The alternate ending for our dialogue is:

Druid: Aww but I really want to be a goat, not a pig. Can't goats behave like that in our world? Pretty please <3

DM: Well sure. Not going to break anything. Go on.

Real World Goats: According to Wikipedia

Fortunately, to get some basis, the Wikipedia has an entire section of their goat article dedicated to how goats behave. No, seriously. Check this out.

Goats are naturally curious. They are also agile and well known for their ability to climb and balance in precarious places. This makes them the only ruminant to regularly climb trees. Due to their agility and inquisitiveness, they are notorious for escaping their pens by testing fences and enclosures, either intentionally or simply because they are used to climbing. If any of the fencing can be overcome, goats will almost inevitably escape. Goats have been found to be as intelligent as dogs by some studies.

So, if the goats in your DM's world behave like real life goats, they are actually an excellent choice for an animal that escaped their farm and is wandering around climbing some trees and checking out what's up with their forest friends.

No checks are necessary unless you try to do something decisively non-goat-like.

There is some guidance in the Dungeon Master's Guide section Using Ability Scores:

When a player wants to do something, it’s often appropriate to let the attempt succeed without a roll or a reference to the character’s ability scores. For example, a character doesn’t normally need to make a Dexterity check to walk across an empty room or a Charisma check to order a mug of ale. Only call for a roll if there is a meaningful consequence for failure.

When deciding whether to use a roll, ask yourself two questions:

• Is a task so easy and so free of conflict and stress that there should be no chance of failure?
• Is a task so inappropriate or impossible — such as hitting the moon with an arrow — that it can’t work?

If the answer to both of these questions is no, some kind of roll is appropriate.

You have to ask yourself, "does my enemy have any reason to believe that this goat that is physically indistinguishable from a goat is not really a goat? Remember, your physical characteristics are exactly that of a goat, therefore unless you say you are doing something non-goat-like, there is a reasonable expectation that you are moving and acting as a goat would. Think about it this way: there's obviously no check required to see if you know how to use this totally unique musculo-skeletal system you now possess to walk around. The ability to move and use your body as a goat naturally would is part-and-parcel to Wildshape.

Therefore, the answer to the first question in the DMG guidance would be "yes, a goat acting like a goat is so easy and so free of stress there should be no chance of failure." It is when a goat starts acting like not-a-goat that checks need to be made: How well can I make this non-goat-like action appear to be goat-like?

To quote enkryptor from the comments:

It's a huge difference between seeing a sleeping goat and catching a goat reading a book.