Can I install a switch on my overhead door opener's circuit for added security?
Yes, a switch that shuts off power to the garage door opener would make it unresponsive to commands from a remote (or anything else, such as a hardwired button). In some models, it may be possible to wire a separate switch to disable only the remote receiver while maintaining the functionality of wired buttons.

You may also look into setting a new code for your opener - this may not help but you should at least ensure the current setting isn't simply the factory default.

Another option, aside from replacing the whole opener with a new model that is more secure, might be to get an aftermarket remote kit and replace the built-in remote system. These are wired like a button control, but come with their own remote receiver and transmitters.

An electrician or garage door specialist should be able to help you with these.