Could it work... I 'think'. Since type 33C/3300 cables are what the 2004 Suzuki would use from the factory, and the OMC, can be adapted to use them... Yes mechanically it might work. As long as the control pushes or pulls the cables in the correct direction, or can be adapted to do so.
As for the electrical side. I would think you have the ignition on the dash, possibly even a 'panel'. Theoretically you could put the Suzuki switch on the dash with an extended harness. You would need the internal harness to the Suzuki/ Johnson control if you have it. Removing the key switch and installing it in the dash somehow would be the easiest way to do it, but a generic switch with the correct function would be better. Suzuki runs their trim harness separate which would make dash mounted trim switches easier
If you are doing this for ' the look' It's probably doable without a lot of fuss just some tinkering.
If you need controls, just buy Suzuki controls. They are inexpensive and quite nice. The basic model they sell will get you boating