Another option (though brittle but possible) is to RDP into the windows machine and map the buttons with x,y coordinates (perhaps normalized). I've had to do this (it wasn't fun) for some games that were Flash AS2 (action script 2, which no one supports including Smartbear, as AS3 came out in 2006).
It wasn't fun but I managed to create a workflow to map the buttons and, in the end, it worked quite well.
You can use the position of the buttons as found on your local PC first and save them out to a file. Then, based on the screen resolution, of the rdp session vs the original button mapping session you can click on the respective x,y coords in the RDP window using LLPlayer.
Like I said, not fun, but it is doable and maybe you can reuse this for the future.
That way TE is not installed on the remote mahcine. It just clicks on the RDP window like a user would. That might satisfy the FDA.
But if you want more info let me know and I'll whip up an example of mapping a single button and the workflow for it so it would work on Windows RDP.