Chances are you have a 7 speed freewheel. I could be wrong there, but even if it was a freehub, I believe the 7 speed freehubs wont fit 8,9,10 speed cassettes?
If you do need new wheels, your frame may not be spaced properly. Todays MTB standard is 135mm, Not sure what it was in the 90's.
It sounds like your trying to cheap out on getting 9 speed as well. You will need/want a new rear derailleur for 9 speed. Front derailleur would probably work ok.
Why not just look for some old 7speed bar end shifters on ebay? A WHOLE lot easier, IMO.