If the outer part of the puller won't screw into the crank arm then, yes you need a different puller.
When you've got the right puller don't forget to make sure the inner part is well unscrewed before you screw the outer part fully into the crank arm. If you don't do that the outer will only screw a few threads into the crank arm, and when you go to pull you will strip the threads of either the puller, or the crank, or both.
When you've got the right puller don't forget to make sure the inner part is well unscrewed before you screw the outer part fully into the crank arm. If you don't do that the outer will only screw a few threads into the crank arm, and when you go to pull you will strip the threads of either the puller, or the crank, or both.