Replacing rear solid axle with skewer

As you have observed your bike has a threaded, solid axle. The wheel is fixed in the frame with a nut on each end of the axle. The Fluid 2 trainer is designed for wheels with a standard quick release mechanism. Quick release hubs have an axle that does not protrude past the frame dropouts and has a concentric hole through which the quick release skewer passes. When you mount the bike in the trainer the special quick release is used which interfaces into the trainer. Older or cheaper trainer designs held onto the existing skewer ends and usually did a lot of cosmetic damage to them.

It is possible to replace a threaded axle with a quick release one, but this means disassembling and rebuilding the hub - not a fun or trivial operation. Another option is to purchase a new wheel with a quick release hub. (Replacing the hub requires a wheel rebuild which will cost more than a new wheel for this level of bike). However, your frame has slotted dropouts which allow the wheel to be moved forward or backward. These do not work at all well with quick releases as you have to re-align the wheel each time the quick release is undone. With a threaded axle and nuts this does not matter as the wheel is not designed to be removed. Additionally a quick release may not have enough holding power to keep the wheel aligned in the slots.

Possibly your best option is to return the trainer and purchase one that specifically works with nutted axles.

BTW, if you undo the bolts the wheel will come out of the frame, but the hub and sprocket cluster will not come apart.

This is not an easy swap.
It would be easier to buy a wheel and freewheel and swap the tire.

As Swifty points out in comments - it's a great convenience to have a turbo tire and wheel to swap in when training.

I looked up your trainer and read the manual. I had hoped that they could somehow accommodate a solid axle - Nope.
It says that you have to use the special skewer that comes with the trainer. The only exception is if you buy the thru axle kit - but you don't have a thru axle.

Swapping to a quick release axle requires special tools
- Tool to remove the freewheel (assuming it's not a cassette)
It might look like this. There are a variety of types depending on your freewheel

- Hub wrench
It might look something like this - just an example
A special flat wrench that lets you hold the cone while tightening the nuts.

I requires the right parts
- quick release axle
- assume your current cones / spacers / nuts will fit on the new axle (no guarantee)
- Quick release skewer

Your current rear hub parts look like this

You would swap those parts with a quick release axle that looks something like this:

The simplified explanation of the steps is:
1. Remove the wheel
2. Remove the freewheel (various ways to do this)
3. Remove the solid axle (sometimes tricky - worn parts, lost bearings, etc.)
4. Install the quick release axle. Adjusting bearings takes some practice.
5. Install the freewheel
6. Install the wheel

If your bike is a 1998 Giant Acapulco it has aluminum 700c wheels that can handle a 40c tire. Quick release front, bolt on rear with 6-speed, 14 - 28 teeth freewheel

It would be easier to buy a wheel and a freewheel and swap the tire.

I have a similar Saris trainer. I tried fitting a solid axle wheel onto it. In my setup the wheel did not securely fit in the clamp. The only thing I think would work is if you could find some domed caps nuts to go the end of the axle. Finding these may be difficult as axle threads are not always a standard thread. Their website did not offer and adapters or solutions. I would contact them to see if they have a solution.

Leave the wheel in tact and see if you can order some 'turbo trainer axle nuts', pictured below, to replace your current nuts on existing axle. If these don't work for you then start disassembling the wheel but research first; you need skinny spanners called cone spanners (£?) to do the job properly and risk dropping ball bearings (annoying). Not normally a huge problem but if bike shops are closed and we're all social distancing atm, then you want to reduce the risk of messing up, temporarily, in case you are left without a functioning bike or help to fix.

Trying to patiently find a solution with low risk atm is reasonable.

I went through the same thing. It was an easy set-up with my Giant TCR which has a skewer. BUT, I'm setting up a second system for my kids and husband's bike which are solid axle. My advice...KEEP your solid axle, add an acorn nut to the end (the side with the gears) - and all will fit and work well.