this can easily be done with technology. An encrypted signal, spread either with digital coding or frequency hopped, can easily do what you want. The problem really is BATTERY LIFE. you want this thing to work when you are within a few feet, but be worn on your clothing and not need to be activated by the user. That means you would need to be transmitting a signal oftn to turn on the spa pump. That will eat up battery life.
If it were me, I would look instead at passive RFID technology, something that has a unique code paired with the one spa, and maybe 3 interrogators around the periphery of the spa, transmitting out all the time, and powering up the RFID chip which will then respond with the right code. Something at 880 or 915 MHz should work pretty well.
the rfid tag would be tiny.
IF you do not like the range you get, you could add a battery and use a powered RFID tag, which would easily work at the distance you want