My right wrist cracks as well. I recently switched to a road bike from riding a hybrid with the type of gears you're talking about. I'm not sure that my wrist cracks as a result of gear shifting, but that would explain why my right wrist cracks but not my left -- much more shifting with the right on the small hills on my commute.
I also tend to get some numbness and tingling, particularly in the right wrist, during long rides...you have inspired me to look for some stretches. The link below contains some decent looking stretches that appear to be designed for those who have carpal tunnel problems (which hits both desk and cycle jockeys; I'm both!!):
http://ergocise.com/wrists.html
Don't know that this will stop the wrist cracking, but I imagine it will help both of us overall.