wireless trigger help

Hi, I am looking for help with a project. I want to create a wireless trigger with a momentary switch, as quickly as possible. Say for example I have a foot switch, and wanted that foot switch to turn on a light for as long as the footswitch is pressed. I have considered using an RC transmitter and receiver, in conjunction with https://www.dimensionengineering.com/products/battleswitch to accomplish this. Problem being I have not found a transmitter small enough to say, cram in to a foot switch. I am wondering if this would be the most efficient way. Could I use a transistor instead? My voltage will be a maximum of 12volts and my amperage will most likely not be higher than 2amps. I have seen a few wireless key fob transmitters with receiver boards on ebay, and have considered that as an option too. But my concern is that I want something that can stay on for the duration of the footswitch being pressed and, I am assuming that that would be a burst broadcast rather than a constant signal. Thanks in advance.