do any shirts fit this bill?

also true

silk or merino wool
Silk is known for its anti-stink properties but of course it is also expensive. I would also look at a thin merino wool. For the latter check out the Icebreaker line of clothing.

Regarding the “stink”.

– Last Updated: Aug-18-15 12:18 PM EST –

DAILY washing, drying & applying FRESH deodorant will help to keep that away or at lease help a great deal with that. Doing so keeps your friends near & dear and willing to have conversations during and at the end of the day.
If possible, wash & thoroughly rinse your shirt daily after wearing. Lack of doing so can set some stains and smells whether from sweat, smoking, or cooked foods, no matter how many times it's washed. Experience has likely taught you about some of these issues.

One word : backwoods
That is not always easy or convenient on multi-day backwoods trips.

What is old is new again
Growing up in Florida we wore our dad’s old dress shirts for surfing and snorkeling. It is cotton which means it says wet and cool.

Cotton is death in the winter but great in the summer. All old dress shirts would be retired to “fishing shirts” and worn for all outdoor activities.

That’s what I used to wear paddling.
Old dress shirts.