The game fully supports the keyboard and the gamepad. Please read the game manual for details:
http://cdn.akamai.steamstatic.com/steam/apps/298340/manuals/F2_Manual_ENG_short_1.1.pdf
As you can see you do not need to use the mouse to activate powerups or weapons - all of them are mapped on the keyboard and on the gamepad.
IMPORTANT NOTICE: If you want to use the gamepad make sure to choose it in the game settings or it will not be fully supported in the game!
Cheers!