It would be much better if you could dismiss people waiting in the queue so that you can keep the queue length sensible... Please change this in the next update. Android and iOS as I play on both.
It is faster to set up an execution chamber inside you vault.
Drop an elevator shaft down far enough so that there is dirt all the bottom elevator room and the elevator room above it. Place one Production room at the bottom. Strip the dweller you want to kill of weapon and outfit and place them alone in the room. Rush the room over and over until the dweller dies.
The execution room is also an ideal place to do the "Kill XX Mole Rats Bare Handed" objective (with the difference that you heal the dweller as it fights).