Yes, your Cruiser can have only one set of TPMS at a time. Since you are going to be switching between sets of wheels and will need a set of sensors anyway, I would recommend spending a little more and buying this
TPMS programming tool and sensors. My discount tire wanted $62 for each sensor, at 5 sensors you’re looking at $310. That tool and 10 sensors is $385 and you can program any schrader sensor.
Again, just something to consider. I have a weakness for tools and hate paying someone to do something I can learn and do myself… 2 really costly but handy traits. Anyway, if yiure going to be switching wheel sets around you may want to consider the tool. This will allow you to make the switch at home. If you’re not the wrenching type and prefer a shop to do this than go that route.