The research
I have the choice of 2 boards, esp32 and raspberry pi zero.

Both boards are great! however they both carry limitations (see image above/below).
esp32 has great radio reach as antennas can easily be attatched. The raspberry pi has a super easy and user friendly connectivity due to its computer like system.

these boards will be the brains of the claw, this will tell the mechanism to open/close when the other device sends a signal wirelessly to the brains - similar to how our brains work (just…not wirelessly :/)

However as the handheld device will be a physical (or digital touch) button I believe the esp32 will be a better fit, this is because it will have a longer range which is needed for drones especially if the drone is custom built, the esp32 also doesnt drain battery meaning the device can be lighter - meaning more flight time for the drone as well as a cheaper system (it wont need a lot of batteries or need larger batteries)

although the esp has a long radio signal it will still need a LoRa addon, this is because of drones signals.