Neoprene fishing gloves... Your hands will be toasty! They are not as bulky as they sound, either. I also have some Champion running gloves from Target, that are a "softshell" fleece that do pretty darn well in wind. I use them mostly for walking in colder weather, have used them on cold weather bike rides, they do fine. Softshell fleece is the most amazing thing...I hate wearing big bulky jackets, in fact I got through most of this winter wearing only a fleece.
I also highly suggest getting your hands looked at. Sounds like some nerve damage or carpal tunnel?