If I were you, I would definitely wear the brace.

Immobilization isn't good for the limb/area that you have CRPS but as you don't have CRPS in your hand, I think the risk vs reward question would lean towards using the brace and treating the carpal tunnel.

You don't want the carpal tunnel to progress to a point where you would need surgery for it; that would be your biggest risk for spreading the CRPS in my opinion.

I'd also be sure that your workstation is set up ergonomically. When I worked at my last position, we actually had an ergonomic specialist who went around at least once a year and did an evaluation of each employees work station to determine if proper ergonomics were being followed; it really is very important.....as they say "an ounce of prevention is worth a pound of cure"!

Things as simple as being sure your monitor/screen is at the right height, that your hands/wrists are at the correct position, etc.

Good luck to you and keep us posted!