Depending on the actual style of t-shirt that has the cap sleeves you might possibly get some of the really wide embroidered eyelet "lace" and create a longer sleeve. I've seen some that would look wonderful on and others that it would just look silly, so I don't know if this would work or not.
For the button down shirt you would need to find a coordinating fabric to add a strip to the sleeve either at the inside seam or down the middle of the sleeve. If you do the middle of the sleeve you could even put in a strip of lace. Either way would require taking the sleeve out and redoing it. (And why do some shirt designers figure we don't have muscles in our arms just because we're female?)
I understand your dilemma as I usually have to get guys shirts for the sleeves to fit right. I hate ladies long sleeve shirts because they are both too skinny and way too short. The long sleeve T-shirts end up as three quarter length on me. So the wrist hits at a much wider part of my arm. Yuk!