The power port will stay alive for 10 minutes after shutdown if you don't open the driver's door during that time. If you need to use it more than that, you have to leave the car turned on. The car will shut down after 100 minutes which should be long enough to charge flight batteries. Or there are ways to bypass the auto shut down.
You can still lock the car from the outside for security and take the key with you. You can turn off all exterior lights, and the engine won't be running assuming you have HV battery charge. It will not be very obvious to passers by that it is on.The only flag will be the dash lights, which can be turned down or covered with a towel. Without battery charge, the engine will cycle on/off a little, or you can charge up with mountain mode.
The good news is that this will protect your 12V battery. No worries about running it down and being unable to start the car. This is really a better situation than you get with an ICE car where your only options are to idle the engine or drain the 12V battery and risk a no-start condition.
If you don't want to leave the car on, my recommendation would be to get a portable jump starter device with an internal battery to power your UAV charger. With this you can also charge more safely away from the car in case of a thermal runaway problem with the UAV equipment. I think it is unwise to tap the 12V battery directly since a no-start on a Volt can be a major hassle. It is not always just a simple jump start like in many other cars.