Can I apply caulk over caulk?
Experiment.  Along one stretch of joint, apply a new layer of your preferred caulk directly over the existing caulk.  If you like the result and the new layer holds up, complete the other walls.  You are most likely to succeed with this approach if you first give the area a really good scrubbing to remove any soap scum.

If the new caulk does not stick, it could be that the old caulk was silicone caulk: nothing truly sticks to silicone (including silicone). 

Regardless, if the result is not to your satisfaction, then scrape/peal/clean the joint really well before re-applying new caulk. 

FWIW, the guy that did my old bath also used the wrong color caulk. As I get older, I'm learning not to trust contractors to handle any aesthetic decisions. :)

(If, on the other hand, you are asking about grout, then that's a whole other question and likely will involve a dremmel tool and a whole lot of dust.)

UPDATE:

Oh, one more tip while we're at it. If you are wanting to match the caulk to the grout, note that many grout suppliers also sell sanded caulk color-matched to the grout.