Wool is the best deoderant around. You should never smell your own body odor in it. In fact, unless I spill something on mine, I typically wear a jersey 30+ times between washes. Fewer if I'm sweating excessively, or kayaking on the sound - both because of salt. On the other hand, some wool can take on the "wet sheep smell" when it's completely saturated. A lot of the high-end exercise stuff avoids this, because the fleece goes through all kinds of chemical baths after it comes off the sheep but before it becomes a shirt. I've got a couple jerseys that used to do that until they've been through several washings, and a few that have never made the wet sheep smell.

I think generally the thinner fabrics are the ones I've had that have never smelled. They're probably also the ones that will be most appropriate for you - least insulation. I'm wearing this one to work today; it's cloudy and might rain later, but around 60 degrees, and I have plans to paddle a kayak a few miles to dinner later on, where I'll get splashed to no end.