I'm using Ursaring as an HM slave with Rock Smash, Strength, and Cut but I'm not sure what 4th move to run. I'm thinking Ice Punch or Fire Punch, but I'm not sure.
I think you should use return (higher base power), dig or earthquake (to cover rock, steel, and several other types), fire punch, and thunder punch. Then, replace fire punch with ice punch after defeating both Pryce and Jasmine. Teach your HM moves to some other Pokemon, so you're not wasting experience leveling up a Pokemon with HM moves.
i'd go with ice punch since it's super effective against more than half of clair's team. but fire punch isn't horrible either.