I went through a long period in my life when i had serious wrist problems. Painting/drawing for hours a day in college, counting money constantly at one job and later on, a job where i sanded and used HVLP paint guns... they all aggravated my wrists and hands. I've tried a lot of things to alleviate the misery. I know what works for ME, so this might help. I would recommend:
-Making sure you are getting all you need in your diet. Especially calcium and vit c. Calcium not only strengthens bones but it makes your muscles able to stretch. Coffee leeches calcium from your body, so if you drink it all the time, you may be low... also, your muscles rob your bones of calcium while you sleep. Vitamin C helps your body absorb the calcium you ingest. You can probably find a supplement will have a Calcium/Vitamin C/some other thing in one pill. My wife loves these soft Calcium chews. Great to take before you go to bed, as the Calcium helps you go to sleep, and you can counteract the whole 'leeching calcium while you sleep' thing. There you go.
-Stretching your arms/wrists/hands, alternating hands when doing daily tasks and keeping in good physical shape is huge. There are some great drummer stretch videos on youtube. It helps. Lifting hand weights or even simple push-ups will build strength in your forearms.
-If you spend a lot of time at the computer, get one of those dumb gel handrests that secretaries use. "Wrist form" at the computer and mouse makes a big difference.
-Dont sleep on your arms. I was doing that all the time and still do occasionally. It sucks.
-Here's the biggie, and the one I CANT RECOMMEND ENOUGH. Bikram Yoga. I tried it three years ago and nearly every physical nuisance or problem i had either went away or can be managed by doing the poses in class. It's hard, but its TOTALLY worth it. It's been magic for my back also, and i know many tattooers suffer from bad backs. This video show the Locust pose which really helps with the hands and wrists. Do two sets of this in the morning and see if it helps.
Thats all I got.
Seriously though. Bikram Yoga. You should see me in the little shorts.