Yep. I put Tiagra shifters on my CC (w/ an SLX rear and Deore front). They work very well, I think. My Tiagras worked just fine with two pairs of canti brakes and now with TRP's.If you want to keep it 9 speed, which is the cheapest option, you will need 9 speed shifters (shimano), new bar tape, and likely new cables and housing for at least shifters/derailleurs, if not brakes as well (these depend on what generation shifters you get). Current sora is 9 speed, or you can go to previous generation tiagra; they can be found nos on Ebay.
If you want higher end, current generation stuff, you are looking at 10 speed for tiagra out 105. To do that, you would also need a cassette in addition to the other supplies.
Sent from a one-finger keyboard...pardon my autocorrect