I'm unqualified to grade Buffs so I won't make a fool of myself.

The coloration seems to be of organic origin, meaning acetone would remove it completely. A lot of organic contaminants - glue, tape residue etc. - tend to acquire that color over time. However, I worry that if you remove it, the surfaces underneath will have aged at a different rate than the rest of the coin and you'll end up with something having brighter areas that looks obviously cleaned. For that reason I would lean towards not treating the coin.
If that color is in any way sticky or tacky, though, you probably ought to give acetone a shot. If you make that choice, mention it here and we'll help you with procedure.