What would happen if I used a 3 speed fan control with a 4 speed fan?
Your 4-speed fan only has four speeds simply because of the remote that it comes with. The fan by itself can work with any controller, as long as the controller is rated to work with ceiling fans.

If you're able to connect your new wireless remote to the existing fan (with no electrical snafus), your fan will happily work with the 3 speeds your remote comes with. It's harder to determine which setting you'll lose, though your highest speed will probably be the same. Individual settings are determined by a controller, and these can vary.

I don't believe you can make adjustments, unless you're willing to open the controller up and experiment with it (not the wireless remote, but the actual controller that sits in your fan's housing).

Do keep in mind, however, that you don't want to use a stepless dimmer with a ceiling fan. That can bring about a whole lot of humming (and more importantly, reduced life for your fan motor).