I would think this may help answer it.
The '01 ZX9R part number for the part in the picture is 44037-1417.
The '03 ZX6RR part number for the same thing is 44037-1442.
I would say no it will not work, but I don't have the actual dimentions, just the part numbers. The parts can be identical for the section that runs through the head/bearing but be different on the lower triple that holds the forks.
IF it works, you are best off with a compete front end including rim, rotors, brakes etc. That would be the simplest swap.
I can't find part numbers on the bearings so check with Kawi, a parts guy can likely tell you if the parts are the same and maybe even the sizes of the bearings.
Don't look good though.:shake