A manual switch to engage cooling is a bad idea because it could be inadvertently left on.
A better solution would be to have a second, basic thermostat. Wire them both in using a DPDT switch. One side would be the radiothermostat side, the other one is your relative stat.
Radio stat - - - equipment - - - relative stat
This way you can't get conflicts between the stats and no manual cooling issues.
Here's an better illustration
You don't need to use a rocker switch like in the picture any number of styles are available.
The key point is that the system is always working off 1 stat. If you wanted to set up the heat the same way you would wire it in a similar fashion but with a triple pole single throw (TPST) switch. They are a little harder to come by but still available in many styles.