Sounds good. Just a quite note about nomenclature -- a freehub supports the use of a cassette -- the freehub is the splined "spindle" onto which a cassette slides and contains the ratcheting mechanism allowing you to coast or spin the chain backwards. The sprockets and ratcheting mechansim are two different pieces.
It sounds like you have a freewheel instead...a freewheel has the ratcheting mechanism built into the sprocket cluster and threads onto the hub. In this case, the sprockets and ratcheting mechanism are one piece and you unthread it from the hub body. Though you can find these in higher sprocket counts (like 8 and 9 speeds), it's probably best to stick to 7 speeds for several reasons.
Good luck!