It won't sound any different due to being covered with a fresh coat or two of paint...and it will look a hell of a lot better. If anything will change its tone, it will be the act of taking it apart and putting it back together and putting on a different set of strings, not the addition of paint on top of it. That tonal change is well within the range of normal inconsistency from pack to pack of strings. So don't worry about these entirely imagined tonal disasters that everyone has laid out for you. Just go for it.