Most "violin varnish" is shellac-based (with denatured alcohol or Bekhol as the solvent). If you're going to use a touch-up marker, you might want to consider applying a few coats of shellac to the damaged area first; the shellac seals and protects the raw wood, and with a barrier layer of shellac in place, if you aren't satisfied with the look imparted by a marker, you have a better chance of wiping it away and trying something else.
When I use "tinted" shellac to make cosmetic repairs, I usually seal any raw wood with super-blonde dewaxed shellac (like Zinsser SealCoat) first because it provides a degree of reversibility; by "tinted" I mean either various shades of naturally colored shellac (e.g., button, garnet, orange...), or shellac to which I've added Transtint aniline dye.
Hope this helps