OK, when you are playing through one head, the other one has to be kept happy...

That means you have to supply a load to the output that matches the O/P transformer, and you should do something to make sure that the input has no signal applied to it. So you need a special kind of A/B switch that can direct your guitar signal to the right input, and also connect the selected amp to the speaker cabinet, as well as making sure that the unused amp stays healthy. This ain't a good time to be "learnin' on the job"!

Find a good amp tech and explain what you want to do. This isn't rocket science, but it will require some fancy switch gear.