If it's a freewheel, you can use virtually any 6S freewheel you want. Any new Shimano one would be just fine. 7-speed is possible but might require more spacers on that side of the axle, and some re-dishing. I'd stick with a 6S to avoid any complications.
And yes there were 6S Shimano cassette freehubs. My friend has one on a 1988(?) Schwinn Tempo with full 105 group.