Is there a way to use these games with AmigaForever (without purchasing a CatWeasel and hooking a floppy drive up to it)?
No, not realistically. Unless of course you have access to a real (and somewhat upgraded) Classic Amiga.
if I were to purchase the CatWeasel is that even a solution?!
At this point it is not because no one has the PCI version of the Catweasel in stock. Unless of course your PC has ISA slots. The Catweasel MK4 will be out in a few months though.