I got rid of my original Xbox when I got a 360 but naturally I kept Morrowind and I was just wondering if the cheats are still applicable simply replacing white button with left bumper and black with right bumper (or vice versa) or if they simply won't work.

As far as I understand the black and white buttons got moved up to the shoulder. I don't have a 360 myself so I'm not sure which one is which. You will probably have to sort it out by trial and error but it should work.

The white button is the left bumper and the black button is the right bumper.

I play on a 360, so take it from me

the 360 contiller is no more diffrent than converting original xbox game codes to codes for PS2 balck and white become R1 and L1

Black is R1 white is L1

convert that to 360 and black is RB and white is LB