Shellac will always dissolve with alcohol, meaning that if you can soak a rag in denatured alcohol and rub off the finish to the point where it changes the sheen [dull] than it's probably shellac. If it's poly I suggest staying with poly. It might also be old style [oleoresinous] varnish, depending on the age of the finish. Does it scratch easily? If it has maintained it's shine pretty well it's probably poly and i would test a spot before shellacing the whole floor.

Jumpilotmdm
Great advice - Thank you
Archie

The problem is that denatured alcohol will also disolve water based finishes and many floors are being finished now with water based topcoats. It will take a bit more elbow grease though to dull the sheen of a water based finish though with alcohol. I think it is highly unlikely though that your floors are finished with shellac unless it's an old finish. Also, why use steel wool? Just sand it.