I have seen more and more mods coming out that allow good classic shooters such as Goldeneye, Perfect Dark and even Doom 64 to use the key board and mouse. Timesplitters 2 is one of the best shooters of all time and deserves this sort of control. Is this possible?
If I recall correctly, I believe most of those mods for the N64 games you mentioned were for a special plugin for PJ64. There isn't an equivalent in Dolphin, as far as I know. The closest you can get is awkwardly using your mouse to control the aiming. Either it's jerky using Axis X/Y or sorta works with Cursor X/Y when you set up the controls in Dolphin. When I say sorta works, that means there is no "auto-center". If you move your mouse left, you don't just look left, you keep turning left until center the mouse yourself. It doesn't play like PC FPS games at all. It's not possible right now, but if you were determined enough, there's no reason you can't hack it by changing the source code (of course, this requires knowledge of Dolphin's codebase and coding in general).
I will say this, you are correct. TS2 was definitely the best FPS experience on the GC, hands down. Never played TS3, so I can't say anything about it.