what you have is a freewheel not a cassette, now for the tool you need is a old Var Schwinn/Maillard freewheel puller(remover). hard to find . you might find one of these at ebay.yes a bmx style freewheel will work for you. since you are working with a one pice bottom backet, there maybe a issuse with the chainline. but if you can run it stright or close to it you'll be fine.