Thanks for the reply.
I picked up a chamois today for 10$ and gave it a try. I believe this is a much better option over the painter’s tape. It seems to grip the blade tighter than the tape.
On a side note, I started playing with the scissor attachment today and found it is wiggly in the mount. If I add the chamois in the vice it takes most of the play out of the attachment. This is a good work around, but I am surprised there is play in the first place.