Cassettes and Freewheels are different beasts. Why not spin off the old freewheel, put a BMX freewheel on the threads and re-space/dish the wheel to be centered?
Freewheels thread onto the hub, and the ratchet is part of the freewheel assembly. In a cassette system the ratchet/freewheel is part of the hub and the cassets slides onto some splines.