While you're correct that the OP has a freewheel, not a cassette, neither of the tools you linked to will work with the OP's freewheel. The OP's freewheel uses the old Regina two-prong design, and needs a different tool. The Bicycle Research CT-1 is one of the better ones, as it has a ring to help prevent the tool from slipping off the notches and damaging them. They've been out of production for a while but they do turn up on eBay often, and your LBS or co-op may have one:



The old Shimano Dura-Ace two-prong remover will also work, but these are somewhat harder to find these days:



It's possible that the locknut may need to be removed from the axle to fit the tool properly.