There are a lot of products that will easily remove dry ice residue. I've often used air, but that'll still leave a slight .039% CO2 film on the surface. Water is excellent, but when it dries, you could be back where you started. I think WD-40 is probably the best thing to use, since it's designed to displace water, and in the process leaves the parts smelling CO2 free.
Putting plants in the shop near the machine will help absorb excess dry ice fumes. Ferns in particular.