Our process is
First headgate the cow, tie a leg back if she is a fighter, so she can't kick you or the calf. Let the calf suck her out, then separate them. We do this for the first day, it helps to get the cow's milk through the calf. From there on it depends on the cow. Some want any calf that they can get, and that may be all you have to do. If she isn't that eager we hobble her hind legs together, be careful you don't get kicked. We use the hobbles with the chain. And, if you have a real fighter put some sort of halter on her. It will save you having to run her down the chute again if she is a bunter too. That way you can simply tie her up for the calf to suck. Did I mention a smaller pen? That is important for a # of reasons. First she can't get away from the calf, second, if you have to tie here up it is easier to tie up a mad cow in a small pen. Usually the cow will accept the calf within 2-4 days. The longest we had took 3 weeks, it was a heifer and we ended up using the figure 8 horse hobbles to slow her down. We won in the end, but I don't know if it was worth it. In rare cases, you may not succeed at all.
I refuse to skin a calf, have done it, and to me it is a horrid job. Most of the cows we have adopted calves on have taken less than 4 days, and I don't think that the hide would have made that big of a difference. Besides which, if you had a sick calf that died, I can't see that putting it's hide on a new calf would be real healthy for the new calf either.