The whole reason that a hand reamer has a long taper is to prevent the thing you're worried about, but if you're using the reamer in a machine either powered of hand-turned, buy machine reamers.

Machine readers can size a blind hole, hand cannot. Hand can be put half way down the taper to provide a force fit. It’s always best to guide a hand reamer using the centre. Hand readers need a smaller reaming allowance to stop them juddering in the hole. I have often used a hand reamer under power, but by pushing the tailstock to give some small measure of float,- not for very small ones though! I’m building a set of both.

And, I would suggest, chucking reamers rather than taper shank.

I use my hand reamers under power, just run slowly as the longer engagement length of the taper may chatter if you go too fast. I hold with a collet chuck in the tailstock when it really matters buy drill chuck if not so critical.