FWIW, here`s what I did for a similar 2 stereo`s to one set of speakers system(1 tube, & 1 SS) requirement :
I have a Mc. original C22 preamp, currently connected(driving) my 2 MC 30`s for occasional use when I desire a total tube equipment driving my Sunroom`s DQ 10 speakers..
But my all day music daily driver for the Sunroom`s DQ 10`s is my SS Mc. C33 preamp driving my Mc. MC 2205 SS power amp system..
Being partially paralyzed, and somewhat lazy, when the mood for the Mc. tube experience would strike me, I wished it to be easy peasy to flip reliably, & safely over to the tube Mc. system without playing with signal inter connects & speaker wire connections.
What I did was purchase (4) 120v coil STDP 10 amp contact rated relays with 3 sets of contacts to allow me to parallel all 3 sets of contacts for a total 30 amp contact rating(yeah I know, over kill !) so that each +/- amps speaker output connections had their own relay maintaining isolation as I didn`t feel combining the 2 different amps negative together was good, or safe engineering to save on purchasing the additional negative wire speaker switching relays.
All (4) of the 120v very low milliamp current draw relay coils were all paralleled together and connected to a 120v power cord, in which I simply plugged into one of the C22`s power switch switched AC back panel 120v outlets..
The relays were simply wired up for the speakers connected to the relay common contactor, and the SS amp output was connected to the NC set of relay contacts(non-energized), and the tube amps output connection were made to the NO relay contacts, and now, and since setting this up over 20 yrs. ago, I make sure that the C22`s volume is turned all the way down before I flip on it`s power switch..
When those, over rated for the task at hand, all those "power contactors" abruptly snap closed , I`m sure to start hearing some good Mc. tube goodness starting in about 30 s.

BTW, before I forget, the MC30`s(or any of my other swapped in) tube amps) have their AC power provided by a smart switched power outlet strip, also triggered by another the C22`s switched outlet, so their never powered up unless the C22`s power switch is engaged..
I only chose to configure this power switch triggered setup not to rapidly A/B flip back & forth between the two different systems, just a very reliable simple system switch over.
There are other reed type relays in another box for routing the 2 different pre-amp`s L/R output/power amp inputs as I have to switch back and forth a a powered Velodyne subwoofer`s line level crossover in & outputs as well, because the DQ 10`s weak bottom octave needs a little help, IMHO.
Anyway like I said earlier, this setup/configuration has been installed and working perfectly for over 20 yrs.
Ciao.