Milder synonyms of "honored" in the "I'm honored" sense

"I'm touched" is a way to express appreciation for something that's a little less strong and/or formal than "I'm honored". It does have some connotation of sentimentality, though, which might not be what you're going for.

Perhaps, pleased works here.

ODO:

pleased ADJECTIVE

1 Feeling or showing pleasure and satisfaction, especially at an event or a situation.

‘he seemed really pleased that she was there’

While this might not be the site where this question can serve as a compendium of sorts for all synonyms, the words flattered or delighted are similar to and milder than honored.

Flatter--To please or gratify the vanity of: "What really flatters a man is that you think him worth flattering" (George Bernard Shaw). American Heritage, 5th Ed.

Delight--Extremely pleased (to do something): I'm delighted to hear it! Collins English Dictionary 12th Ed.

It seems that it will be hard to garner definitions that really gauge the degree of potency different words will have in this phrase, as they're often subtle, having changed over time, becoming cliche or shifting by associated usages, and different from the word standing alone. Plus they may often even vary just based upon challenging context changes. Consider even the phrase "thank you", it can be a passive (even dismissive) phrase just to meet cultural expectation... or can be used with passionate or intimate deep-seated gratitude. Many phrases will change meaning in different locations or contexts.

I suppose my best suggestion for trying to convey your lack of passion would be I'm appreciative. "Appreciation" seems more generally seen as a more middle-ground response, in comparison to responses like "awe" or "overwhelmed". Acts that go more in hand with appreciation to me are applause rather than ovation... and a thank you card rather than a deep debt of gratitude. A lot of this may come from the word being more conected to an intellectual response rather than an emotional response, as indicated by many of the related usages of the word...

-The act of estimating the qualities of things and giving them their proper value.
-Clear perception or recognition, especially of aesthetic quality: a course in art appreciation.
-An increase or rise in the value of property, goods, etc.
-Critical notice; evaluation; opinion, as of a situation, person, etc.
(Dictionary.com)

Ironically, another option might actually be I'm thankful. Despite the opportunity for the word to convey deeper meaning as noted above, it seems to be taken as rather basic and minimal in such usage. Usually a more emotional gratitude has additional indications, and in isolation is best heard in a voice rather than in text. I believe, at least here in America, someone who is really moved will be driven to find a more emotive word than simply thankful. Alternatively, to even more give a basic appreciation without any sign of depth to your response, I'd just go with thank you or thanks as being very basic, and having the benefit of avoiding introducing you as a subject into the topic at all, any usage of which may signal an extra response.

To me flattered, delighted, hono(u)red, and touched all show much more passion than thankful or appreciative. But I believe all such phrases will subtly vary depending upon your location and audience.