Sorry - I assumed a level of knowledge with the ham background.
There are three common frequencies for these kind if transmitters. 434 and 868MHz in Europe and 434 and 915MHz in the US. They nearly all use on-off keyed AM, and are frequently connected to an IC to perform encoding, generally with two or more switched channels and some kind of address to avoid conflicts between systems.
These only have a few pins and are very cheap - you could probably buy one and drop it in.
If it is more complex than that, most devices have an FCC ID. This can be looked up online, often providing photos, a technical document, and sometimes block diagrams and schematics. You could find out what it currently uses and take it from there.