Since you want a short sleeve shirt similar to a base layer top, go to any specialty running store or even Sports Authority type place and look at their tops. I know you said you didn't want an Athletic cut, but you can buy a size larger or get a standard T-shirt cut. Many brands from Columbia, Champion, Nike, Asics, Under Armor, etc have lightweight shirts in coolmax, drifit, etc material that wick well and have both SPF and anti-microbial protection in the fabric.
If you're willing to try a long sleeve shirt, I like the Columbia PFG hiking shirt, which has the SPF and anti-microbial fabric. It's not a base layer, but it wicks well, dries quick and keeps me cool in the sun and warm in wind or lower temps. It also doesn't smell bad with prolonged use between washes. Infact it dries so quick that you could just rinse it in a stream and put it back on and it will dry within minutes. You can roll up the sleeves and secure them with the little button tabs. There are a few different styles, I prefer the snap front because it is also lighter weight than the button down style and it has better ventilation. I have found Columbia products in the US market to be lacking in quality and functionality, but this is their one product I really like and haven't found anything better, especially for the price. Retail is usually around $45.00.
Similar shirts can be found from RailRiders and REI, but may cost a lot more.