I bought a Win 94 in 82 and have never taken it apart.
To clean I just run a brass brush with oil down the barrel a few times then a dry patch. I repeat that until the patch is clean. After 50 or so firings I'll use copper solvent and a nylon brush to get the copper fouling out, but usually get next to nothing.
Since I insert my brush from the muzzle, make sure you are gentle with the crown.
Winchester Model 94 Disassembly