You can play without a joystick, but itīs quite difficult without one.
To set up your mouse for flying, take a look at
http://www.hitechcreations.com/gs/index.html (Look at Configure joystik or a mouse)
If you have any intend to play this game for a longer time, get a joystik. It doesnt have to be an expensive one, any cheap stick with a so-called "hat" will do. (Just stay away from Logitech, though)