The difference between a hand reamer and a machine reamer is that a hand reamer has a longer lead in taper than a machine one.
If you want to an adaptor so that Morse taper tooling can be held in your machine, you can buy sleeves with an internal Morse taper and a plain OD.
They are available (try RDG for instance).
The problem might be that the OD of the plain sleeve is to big to be held in a drill chuck in the tailstock. In which case, you will need an adaptor to carry a lathe chuck on the tailstock, to accommodate the larger size.
Overall, I would suggest that if you have to make adaptors, while you are about it, you make the reamer holder floating, so that it can follow the hole.
If the reamer is held rigidly, and is off centre, it will act like a boring tool, removing more material from one side than the other, to produce a hole that is oversize.
Howard