Have you ever used a separate speaker selector unit to audition speakers? Would you?

Look, no one would put a switch box in the signal path for no reason. But if you need to compare gear it’s a much better way than powering up and down and swapping cables.

This is the only reason I would put a switch box in -- to try to make a comparison. Then, I’d set it aside. Regarding @b_limo point about variables — the idea would be to use the same cable and keep the other elements as similar as possible (positioning, room, etc.) It might be necessary to quickly move the speaker being auditioned around a bit — but that can be quickly done, compared to the amp on and off rigamarole.

Of course, if the switch box isn’t high quality, then I could be degrading the sound too much for both speakers and erasing important details which would be crucial to their character — and their difference.

It seems this is another debate that rests upon empirical details not fully definite -- which speakers, which switch box, etc. I don't have the speakers yet, so this is impossible to detail, yet. I'm trying to decide on buying a switch box.

Another option is for me to get a switch box and try both. If I hear no degradation of sound with the switch box on either speaker, I can go ahead and compare them.

I have the Adcom. It allows 3 pairs of speakers to be switched from one amp. 

For convenience, absolutely.

For differences that are so subtle / minor, yes...as I believe time and memory are not always on friendly terms.

For retail or industry reasons, yes.

Etc.

I believe learning to ’hear’ ’listen’ with greater accuracy and differentiation is valuable and worthwhile (both as pursuit and goal) and has been incredibly rewarding for me. Working on this has helped me dig much deeper into our hobby, understand it better, and has made it much more enjoyable.

If the box helps you do that, go for it...push yourself to make it more than simply a tool to compare speakers.

 "I have a tube amp that requires shut down, short break, between speaker changes"

What is the reason for the shut down?

The reason is he doesn't want to fry his amp which is what will happen disconnecting speakers with it turned on.


Meanwhile....   

Anyone concerned about not being able to compare or judge because they will forget what they heard in a few minutes should stop and think about that. Ask yourself, if you really can't remember, then why would you care? If you have no memory of something better, how can anything be worse? Seriously. Think it through. Why would you care? 

Look at it another way. If the difference isn't big enough to be sure, how could it possibly be worth paying for? Might as well buy the pretty ones. Which if you can't remember, probably what you're gonna do anyway. So why bother?

Anyone concerned about not being able to compare or judge because they will forget what they heard in a few minutes should stop and think about that. Ask yourself, if you really can't remember, then why would you care?

That isn't the issue, the problem is you have no music in the hour(s) that wait for the tube amp to cool down and warm up.
A high quantity speaker A/B switcher is the solution, but you have to make sure the tube amp output is connected to a load at all time while power on.
A safe way to swap is mute the input, if the switcher is on speaker A, select A+B first then change to speaker B, so the tube amp will be loaded while swapping speakers.