I think your hand is easier to play if you raise flop to 4-5$ and then check it down
You can play that way, butt hen you face probably every times river bet and at that case it is overbet and you can´t call, since although his range is Ax or nothing you´re not getting great odds and have to be right close to 50% that he is bluffing
Don´t think he would take that line with KK or Tx too often