I'd love to be able to do that (and in fact it was in the CK protoype!) but unfortunately Ren'py (the SDK I use) is a 2D engine, which means that all the animations are baked in - which means I can't hotswap models around in animations as each one has to be rendered out as a movie file.
I tried just making variations, but since I'd need to include at least four skin colours, and create appropriate variations for every single scene the MC is in, it inflated both my workload and the game's filesize way beyond what a solo dev could handle, and would have shrunk the amount of content each update got.
So unfortunately, due to system limitations, changing the MC's skin colour isn't possible in CK. Sorry! I'm looking into alternative engines for my next game, though, so keep your fingers crossed!