OK,
What I suggested could work, although I'm sure there are units that are designed to do this job, but much more expensive.
If you have an old/small/light keyboard that can store and load a midi file, from a disk or a USB stick or suchlike, and then send it, then this could do the job. But not one keypress, if you need to load different files at different times and then play the file.
You'd need to make sure that the unit you use will send data on ALL channels.
Does your main keyboard do this anyway? If it will store and 'play' midi files, then it will. You say it will play notes as well? Why? The midi file I'm thinking of will contain ZERO notes, but PC (program Change) commands ONLY. Playing this file will make no sounds. I assume you can make such files easily, I certainly can.
Geoff