I accidentally used quickcrete mortar instead of cement. The bags looked identical. It is obviously not sanding the same. Can I sand it down and skim coat it with cement and sand it again?

No you cannot. A skim coat will fail in short order. Its a case of proper bonding that is the issue here.

I suggest you go to the Quickcrete web site and ask this question to their team of experts. Perhaps they can advise you but my experiance tells me that a skim coat will not wear or finish properly.