I would not change expensive inlets. I would not carve up expensive generator cords, unless they are already homebrew (field-assembled) and already have a replaceable socket.
I would build or buy an adapter cable that has a plug that goes into the generator, and an inline socket that accepts your existing 4-wire cable.
If you build it, you will need to learn a lot more about how split-phase AC power works, because you have tons of stuff totally wrong about that. Let me hit the high points.
Neutral is not ground.
Safety ground is a safety shield that never carries current (unless there's a fault, obviously).
Current flows in loops. Neutral is the normal way that 120V current returns. It needs to be separate from ground because Bad Things happen when they are combined.
North American power has two hots of 120V each, opposite phased.
And for a technology briefer on that, see this video.