I haven't had much success trying to make 120 spools fit 620. Not only is the size different but the slotted holes in the spool ends are different too. This causes the tailored spool to bind often enough to be a bother. If you have a camera that takes 120 and has no shutter linked stuff on the film advance, first load it up and crank the entire roll across. This makes the film and backing paper nice and snug. Carefully remove then hand wind the film and paper back onto a 620 spool in total dark of course. I start the paper in subdued light to get it on the spool straight for 3 - 4 turns then continue in the dark. If you wind carefully and tuck the free end of the film smoothly along with the paper the film won't bunch up any more than 1 - 2 mm at the taped (frame 1) end, a small enough bump to not get hung up anywhere. I had some old film around to practice on which was a help. Goes without saying, guard those old spools carefully, expect they are available somewhere but...
Gotta love those oldies.