yep, a SPDT switch would work.
just so you know, two of the three wires on your RTD sensor are looped together, essentially a 'jumper'. its so that the controller can factor in the lead wire resistance into its temperature conversion. RTDs work on resistance of the probe, so the legnth of wire attached to them will change the measured probe resistance. the 3rd wire is used to remove the variable of wire legnth.
since we dont need a 100th of a degree of accuracy, and really 1 or .5 degree is good enough, (and some PIDs dont even use this wire) you really only need to connect two of the wires on the probe. that gives you more options for switches.
possible, but ive done that several times with a few of my cheapo (lightobject.com) PIDs and it works fine. that does not mean that it is best practice, but it shouldnt damage anything. an RTD probe is just a resistor, so if the PID is normally sensing a resistance of, say, 10kohm, and all of a sudden the resistance goes up out of measurable range (when you disconnect the probe its essentially infinate resistance between those wires), it should just report an out-of-range error.
any problems you might have would only be from the PIDs ability to sense when the resistance is back within measurable range. you may need to power cycle some PIDs before it picks it up again.