There is a possible way I think that could work , it would have to be tried. I have never tried this myself with a CPU, but I have with some logic chips, but it would be something I would try before making a more complex system to switch in more than one CPU.
It definitely won't work doing by de-powering one CPU, because what happens is when a pin is pulled high on the non powered CPU from the powered one, current is sourced by the input protect diodes into the non powered chip die. Actually similar things happen in that if you switch off the CPU's support chips, then their inputs draw current from the CPU or other chips driving them, because often the internal resistance of the power supply system can be fairly low when de-powered, not so much if open circuited though.
(Coincidentally, I just had a really interesting issue with an mcu, that draws a significant glitch of current when its support chips are de-powered when the unit powered down. In this condition the MCU itself is powered by a backup battery, but the glitch was pulling the supply pin low enough to corrupt the RAM in the mcu because of the higher internal resistance of the battery supply)
Also, everyone is familiar with the story of the cmos chip that still works, even though you forgot to connect its power pin to V+, because it becomes powered by one of the other inputs which is high via the substrate diode/s, so if all pins go low, the chip stops.
In any case, what you could try:
With the two CPU's wired in parallel, you open circuit the earth pin/s of the CPU that you don't want (and also any other pin from the CPU package that are connected directly to ground, connect all these together to the switch).
The idea is that you create a situation where the remaining connected (deactivated CPU) pins cannot sink any significant current to ground. You can use a switch or a transistor acting as a switch, then the CPU's GND pin/s pull up to +5V with the switch open. This de-powered chip could attempt to be powered by pins pulled high by devices they are connected to, but they will not draw any significant current because the input pin is a diode drop below the +5V supply. Meaning they would have to go over 5V to get any current into the chip's pin.
But, in this condition, can any pin on the deactivated CPU sink any current from the other working CPU pins ?
There could be a current pathway from one pin, to another pin in the package, but given that the CPU that is off is un-powered and has no solid ground connection, it is likely to be only a very weak interaction and not affect any of the lines on the active CPU. The input substrate diodes would conduct with the input pin pulled low, so that would create a weak pullup effect (most likely), if it was too high, then a switch could be made to open circuit both the ground and power pins of the deactivated CPU. That would be an interesting experiment.
As mentioned, this is a possible way that could work, it would need to be found by experiment and looking with the scope if there were any significant effects at all from the deactivated CPU affecting the active one. And if it did work, you would still need a reset for the selected active one.