Sun Shirts; A lightweight base layer with breathability, UV protection, and Doesn't stink

I have not been able to find one that is lightweight and doesn't stink after a few uses.

Has anyone found one that's made of wool that also breathes well? Any suggestions?

Uses: backcountry skiing on a warm spring/early summer day and as a base layer for long multi-pitch climbing days in warm weather.

Check out https://www.icebreaker.com/ they don't stink. Some guy sailed around the world in one of there shirts and never washed it, did not stink (Marketing campaign). I own several Icebreaker items and can attest to this.

Merino is the best combination of UV protection and stink resistance. I've had great success with the Voormi River Run Hoodie and Icebreaker Sphere LS Hoodie. BD Alpenglow is a great synthetic option, treated with polygiene and I've found it does seem to work to resist the stink for at least a day or two. For the hottest days I find wool too warm (and the Alpenglow), found the Patagonia Sunshade to the best option, haven't had odor problems with it.