Update: I bought the tool. Put it on. Turned it with my fingers and it came right off. Since it was a new wheel (oops, didn't mention that) it was never tightened at the factory.
Odds are I will never need that tool again, but I now have a nice new Park single speed freewheel remover to help others with.
Thanks all for the advice. Yes, if it had been tight, I might have royally buggered it up with the hammer and punch.