If you can get a shot at him, I think the gun is the way to go. Poison and traps don't discrimminate. Only a person with the ability to reason with their finger on the trigger can do that. I'd rather not have to deal with releasing a non intended catch, or the consequences of a killled or maimed dog, cat , bird or anything else. You reasoning is sound to make sure you are dead nuts at that angle and range, and figure a way to quietly open the window to get a shot. Even if you trap it, you will have to shoot it in the trap, which is not that pleasant of a task. No one in their right mind will let you relocate it near them. I prefer my .17 WSM which I used to kill four groundhogs and a raccoon in the first month of owning it. The .22 ought to be up to the task at that short range, and as always, you use what you have. Everyones situation is different. I don't worry about neighbors on my 471 ac, but with how well you've thought it out, you have considred all these factors.
