I don't think the Gerber Gator's rubber handle (may also be something called 'Kraton', IIRC) will be damaged much, if at all, by some sparing use of paint thinner or mineral spirits. Being a relatively modern knife, most synthetics these days are engineered to be pretty resistant to most common solvents, at a minimum.
You might just moisten a rag with paint thinner or mineral spirits (or even a Q-tip, if the paint spots are minimal), and scrub the handle with it. No need to soak it, most likely; that's the only thing that might damage it, if it were immersed or soaked for a lengthy time.
The paint might also be loosened up with some WD-40, which also is quite mild and shouldn't damage it. Use it the same way as described above.
David