But then that would oath up your opponent's creature that they are playing, which may be bigger or better than yours.
Damn, you are right! What about using a creature like the Rainbow Efreet, which can phase out when the opponent's oath triggers, but which can attack during our turn? Maybe to slow to kill the opponent? But it also has the advantage of being hard to remove.
P.S.
However, against non-oath decks which play the claw, having creatures which are more easy to cast (mana drain can help) would be better; along with more removal spells. With the current build what can we do against a chalice for two, a meddling mage or a cranial extraction? Having an alternative win condition besides oath itself is needed. And even some sort of removal, maybe Engineered Explosives or rushing river?