While in game as soon as I press to start recording with FRAPS, the mouse movement (aka ship movement) greatly increases speed as if I increased the DPI by 10 times. Not only that, but at times when I move the ship very quickly on my own, the game just skips and I find my ship on the other end of the screen etc.

As soon as I stop recording the game goes back to normal behavior.

Any suggestions on how to fix this?

I recorded a session to show how fast the ship moves and the rest.

https://youtu.be/eiOVsVtbJDQ

FRAPS is a moribund program, it hasn't updated for a very long time.

I'd suggest you look into a different program like OBS or ShareX.