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.
From what you've described, this is what I think you're wiring should look like. Keep in mind, this is just a guess. I can't see what's going on, and I'm an internet away, so I can't touch/measure/test anything.
![My guess at wiring](https://i.stack.imgur.com/wfpIw.png)
The wiring diagram for the switch, can be found in the installation instructions.
![Wiring Diagram from Installation Guide](https://i.stack.imgur.com/j3yej.png)
If you provide images, and/or a better description of what wires and cables are in each box. I'll be able to provide a better guess, as to how this should be wired.
NOTE:
The diagram is based on your description, and is my best guess as to what your wiring looks like. If you're not sure what to do, or feel like this project is over your head. Do not hesitate to contact a local licensed Electrician.
Best Answer
Per the installation guide:
The blue wire from the receiver won't be used, so just cap it. (This would be connected to a blue wire (or possibly black with white stripe wire) if your fixture had a fan)
Connect the black from the ceiling box to the black on the receiver