The switches for the fan are either in the lower bell housing or on top of the motor assembly.
Check the lower bell first. There should be 3 or 4 small screws holding this on, remove them and carefully remove the light assembly. Look inside the bell to find the RF receiver, the switches are on this (you may have to pull it out to access the switches).
If the RF receiver is not there it is probably on the motor assembly, in which case the fan will have to be taken down. Even if you have to take the fan down you should not have to disconnect any wiring, there should be a hook on the assembly so you can hang it from the mounting bracket while you adjust the switches.
Depending on the ceiling clearance you may have to remove the blades, then remove the decorative ring near the ceiling. Carefully remove the screws that hold the fan to the mounting bracket, you should be able to hang the fan from a hook on the mounting bracket (so you don't have to hold the fan while you work). Inside this assembly you should see the RF receiver, adjust the switches and re-mount the fan.
The short answer is that it depends on the internal circuitry of the remote. I have a Harbor Breeze fan/light combo that came with a wireless remote, and I know that there are protective circuits inside the receiver that detect if there are non-incandescent bulbs in the system (e.g. CFLs/LEDs, which can cause power spikes, don't work with simple dimmer circuits, etc), or if the wiring is connected incorrectly. This protects against certain short-circuits and against overloading the wiring. From what I know, the basic design assumes you will either use it for a fan only, or a fan with light.
If this is the case, you can't use the remote to control just a light. The receiver will detect that the motor circuit is discontinuous and shut off to protect itself. However, the receiver may not be that "smart", so as long as the Motor Hot wire is capped off to avoid arcing, shorting and electrical fires, the circuit through the Light Hot and Motor/Common Neutral wires should still work. You just have to connect the receiver unit properly; the wires coming out of one side of the receiver should go to the J-box, matching white to white and red or black to red or black, and the wires in the other side should go to the light, again matching white to white and black or red to blue.
If this doesn't work, you're probably going to have to put the light on a wall dimmer. There are models of wall switch that are also receivers for remote controls. Lutron's "Maestro" system uses one wired wall switch, to which a number of wireless controls can be linked and communicate with it via RF. This allows for, for instance, 3-way switching where there used to be none, without having to fish wire. In your case, the Pico remote control works with a Maestro switch and allows similar functionality to what you want with the Harbor Breeze control; a remote you can take in hand and control the lights from anywhere in range of the wall switch. You can get this system at a Home Depot or online. Downside? It's toward the cutting edge of home lighting controls, and so is pretty high-end; the switch and remote control combo is about $80.
Best Answer
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).