My experience is that most 620 cameras (I have several, Brownie Hawkeye, Kodak Reflex II, Adapt-a-Roll 620) will accept a 120 supply roll with the rim of the spool trimmed down flush with the paper backing. I've seen a number of references to some cameras being tight enough that they won't accept the very small extra length of the 120 spool, and some folks have sanded the spool flanges thin to accommodate this. With flanges trimmed for diameter and sanded for thickness, any 620 camera should accept the result (and a few might be able to use the empty spool for takeup, if the advance key will grip) -- but the effort to make both modifications, to every roll of 120, seems to me more than what's needed to respool the film. Of course, if you don't have any 620 spools...
BTW, a couple of the online film sellers offer fresh film that's been respooled for you, at a price that seems reasonable when you consider they include a genuine 620 metal spool (commonly $10 empty if you can find one) as well as the labor for someone to get the film wound the right direction onto that correct spool. If you have a camera that's so tight it won't take a diameter-trimmed spool, I'd be tempted to get at least one roll of this stuff, so as to obtain a second 620 spool for your own respooling.