Most likely. It sounds like a Traditional Rifle - straight stock, 20" bbl. Later on Winchester added the Black Shadow and Timber Carbine models that wore pistol grip stocks (had a bit of a downturned grip). The Black Shadow was a plastic stock with a 1/2 mag tube and the Timber Carbine wore wood but with a 18.5" bbl. HTH.
I think you would have to contact Winchester to see if they have any different stocks left laying around for that rifle. If not, I'm certain that some of the links on our links page here will get you to stockmakers who can provide what you want, as long as the tang on the rifle matches the stock configuration you want.