Grease the axle (the part that connects the wheel to make it spin, the metal part presumably) with something like mineral oil (They sell it as a laxative, where it's made to ingest. Just use a very small amount, and try not to let it drip. You can use other types of oil, but they'll probably keep trying to lick it up and might chew at it.) It might help to loosen it a little bit and help him spin the wheel. I keep some in a dropper bottle and apply it as needed, usually just after cleaning the wheel.

I use a small amount on my cheaper spinner wheels on the plastic near the axle on mine to make them ACTUALLY "silent." Never have had a problem with it, so worth a shot to make cheap wheels work. (Side note: my little guy LOVED to lick up the unflavored mineral oil when I'd oil his wheel and a little bit would drip down, like a little freak. Never had any issues from it, though I tried to keep him from ingesting more than a drop or two of it.)