Depends on the finish. If it's polyurethane, then T-Cut will be perfect for the job.

If it's an older (or more expensive) fiddle, with a proper shellac or 'button' varnish, T-Cut will ruin it, as it removes the surface layer. Careful work with warm, soapy water should do the trick. Obviously you don't want to get it wet - just dampen a cloth enough to remove the varnish.

In extreme cases, diluted vinegar (about 2:1) can be used.