I think using Shadow Claw on Chesnaught makes sense if you're trying to use it as a counter to Mega Gengar. Hitting for NFE damage isn't exactly desirable for a counter. You could also mess up a Dragalge by switching in on a Sludge Bomb and hitting it with Dragon Claw. Doubt your opponent would be expecting that, since no-one uses anything other than defensive utility on Chesnaught.
Actually, I think Chesnaught as a whole is a Pokémon designed to be used as a counter. He will suffer 4MSS no matter what he does; he cannot cover all his bases. That leaves the question of what you do want him to cover, as that can be any of a number of things thanks to his massive variety of offensive types. That probably depends on what your particular team is weakest against. Whatever physical-based opponent (or Special-based for certain cases like Lucario, Mega Gengar, Dragalge, etc.) you use him to counter, he'll generally be very good at it, as long as you remember that his "viable counters" list doesn't include Talonflame, Mega Pinsir, or Fire-, Psychic-, and Fairy-types in general.