I bought one of those for my Carlton recently because the original Suntour didn't survive being removed from the old back wheel. At the time it was the only 6 speeder of nearly the right range (I wanted 13-24) I could find on
eBay, obviously from the moment I pressed "Buy" eBay has been awash with exactly the right model. The no-name effort felt quite shoddy from the start and has only been ridden far enough to go through all the gears. I am currently awaiting delivery of a badly listed Suntour (1/4 of the price a well-listed example fetched the day before).
Freewheel removal without the tool is actually quite easy. You just unscrew the bearing cup/locking ring with a hammer and screwdriver (can't remember which way but it quickly becomes apparent) and pull the cluster off. Then it's just a matter of using a pipe wrench type tool to undo the centre part. Brutal but effective, and it
can be done non-destructively if you want to put the freewheel back together again. In your case the freewheel will never be any use until it's been stripped down and rebuilt anyway so you have nothing to lose.