Have a lot of options.
You can use EWS from One together with ECU of One and the Start Switch and coppy the map from Cooper to One ECU, but probably are different sw and car will not start or tool will refuse to write.Need some skills to write a good file.
Second is to coppy Cooper eeprom from EWS and made a new chip for key fob.Install the new chip in Key fob from One and use learning procedure for open and closing doors.
Third is to make immo off in Cooper ECU (need boot mode)and use key fob from One together with Start Switch.Same procedure for closing doors opening.
Minis never die.They just get faster
If you speed up on curves instead of slowing down you probably own a MINI Cooper.