Thanks for your help. Unfortunately, that only disables those keys when I was not in the game leaving me without arrow keys otherwise. When I slept on the problem, I remembered AutoHotkey and was able to do what I needed there with the following commands (for anyone curious):
#IfWinActive ahk_exe ShooterGame.exe
Left::MouseMove, -1, 0, 0, R
Right::MouseMove, +1, 0, 0, R
Up::MouseMove, 0, +1, 0, R
Down::MouseMove, 0, -1, 0, R
#IfWinActive
So basically, if the "ShooterGame.exe" process has focus, change the arrow keys to move the mouse. If it doesn't have focus, no changes are made to those keys and they function as they normally do.
Thanks again for your help.