Depends on the type of paint used, any preparation that has taken place prior to painting and the varnish type used on the blank itself.
My first attempt would be a quick wipe with iso propyl alcohol, which can soften some paint types. If that doesn't shift the paint then step up to cellulose thinners - which usually works. Be careful not to strip the original varnish, which may soften or in the worse case be removed. Avoid undue exposure of the solvent to the blank and yourself.
Could also try nail varnish remover - this contains mostly acetone and is easily available in small quantities.
Usual safety measures - don't breathe fumes, do it in a ventilated place, wear gloves and no sources of ignition.
There are countless other methods, but the ones I mention usually work.
As Mike suggests, gently picking the old finish off can work.
See how you get on,
Cheers
Bob