It is important to check props for balance, but it's actually not overly important to have them perfectly balanced.

If I were you, I'd check over that balancer closely. And I'd try it with a couple of other props. And I would have no reservations using that prop if it was only moving slowly such short distances. But veryify that the balancer can and will find an out of balance prop dependably. Put a bit of masking tape on one blade of that haunted prop and see if the balancer dependably points out the taped blade. Test the balancer to prove it works dependably and go from there.

Most of today's props are going to be pretty good for balance. But it's "expertly sensible" to check them. And same with the balancer. Check it out.