Luke is correct, you can mix different motor oils. They will mix their viscosities, so they won't be the same viscosity, but they will both work, together. The engine, and the transmissions, share the same oil. All motor oils can be mixed, without ill effects other than viscosity issues.
The Shell T6 is a high detergent oil, so with regular use, it will do an excellent job of cleaning your engine, and transmission. If you want to scour it clean quickly, add
SeaFoam, as per the directions, to the engine. Run it for 5 minutes on the centerstand, shifting through all five gears,
idling, then shut it off, and check the color of the oil on the dip stick (if it has such), on a white rag. Your oil will turn black if the engine and transmission had carbon deposits, from age, and oil breaking down with use, over time. If it comes out clean, then it isn't necessary to change it. But do monitor it for 300 miles, or so, to see if it does blacken -- then change it immediately. Cheers!
1979 CB750K (sold, 2012, but not forgotten)
1983 Kawasaki 440 LTD Belt Drive (sold, 2011)
1993 Kawasaki Voyager XII