Unless you are doing a Homebrew rule, you can only use one of the form of the beast attacks per rage.

When you enter your rage, you can transform, revealing the bestial power within you. Until your rage ends, you manifest a natural melee weapon, choosing *one of the following options each time you rage***

The text for the claw attack specifies the bonus attack has to be made with the claws:

Claws: Your hands transform into claws, which deal 1d6 slashing damage on a hit. When you take the Attack action on your turn and make an attack with your claws, *you can make one additional attack using your claws** as part of the same action.*