I have used wheels on a drill press, but it is very awkward and dangerous because of how you have to hold the razor and the interference of the chuck.

It can be done, but a dedicated buffer is probably the safer, with lots of clearance, that you can hold the razor with both hands and it gives you a good view or the buffing surface while buffing.

It is still dangerous but all the other caveats apply. I still do both. Though lately, I do more hand sanding and use the buffer with 600 and greased compounds to finish.

The best advice, is live with some defects and buy better razors.