If I was doing this job professionally for beer tokens+ vat what I would do is:-
Chuck the 8″ diameter upper wheel in the lathe and set it up dead true, if necessary in a four jaw chuck.
Set the spindle speed something like 200 to 250 rpm – forward rotation.
The 8″wheel is described as hardened, however, you do not know how hard, or whether it is case hardened or through hardened.
To me, that rules out carbide radius tools, you don’t know what you are up against.
If it digs in or chatters you are bust.
I would procure some 125 mm flap discs for your angle grinder in fine grit size more than 300 grit and gently work the radius round with these discs, with the work turning at the 200-300 rpm referring to a radius gauge.
The images of these 8″ wheels from USA sites seem to suggest that the edge radius is about an 1/8″.
The finer the disc the less it will take off in a pass so less chance of a f*** up.
Finish off with fine emery or wet and dry paper + oil wrapped around a wooden stick, not a file, if it slips it might gouge the work piece.
Just my two pennyworth !!