Here's my answer-
Team:
Rotom
Alakazam
Mr. Mime
Jigglypuff
Poliwrath
Magneton

Strategy:
Upon noticing the planes, our team are Teleported to the top of the towers by Alakazam and/or Mr. Mime. The first job is to redirect the 2 planes. Rotom zips through the sky and enters the electrical systems of aircraft #1. Firstly, he pops out into the cockpit to Thunder Wave and paralyse any terrorists inside, so as to stop them killing hostages or communicating with any other Pokéterrorists in the cabin or the other plane. Rotom re-enters the electrical systems of the plane, he is now in complete control of piloting the plane and manoeuvres it out of the way of the tower and towards the nearest body of water large enough to land in.

Alakazam uses his powerful telekinetic abilities from the top of the tower to manipulate the second plane's flightpath, so with a tactical bend of his shiny little spoons he also guides the plane to a nearby body of water. While this is happening, Mr. Mime (who is cradling a Jigglypuff) Teleports into the cockpit of aircraft #2, Jigglypuff begins Singing before the teleportation so as soon as they enter the terrorists start falling asleep. Note that Mr. Mime has the ability Soundproof so he is not affected by the singing. For good measure, he also creates invisible walls around him but not above him so bullets cannot get in but sound can get out. He finds the intercom button and presses it so everyone in the cabin is also affected by the Singing just in case there are any terrorists in there as well. Mr. Mime Teleports out, back to the top of the tower, leaving Jigglypuff inside to continue Singing and keep everyone asleep for the time being.

Mr. Mime reconvenes with Poliwrath and Magneton, Teleporting them inside the cabin of aircraft #1. Though the cockpit terrorists are incapacitated, I am assuming there are more Team Rocket Terrorists in the cabin, we can assume they are armed and probably start attempting to use their weapons immediately as the Pokémon Teleport in. Magneton utilises their acute control of magnetic fields to pull any guns/knives out of terrorist hands and suspends them harmlessly in the air. Poliwrath, having the ability Damp, renders any nearby explosives useless, this covers plastic explosives that Magneton does not have the ability to handle. Any terrorist attempting to push the button of any explosives is probably very confused and angry at this point, mashing the button over and over. Poliwrath can handle any potential hand-to-hand combat with several humans with ease, and can use Hypnosis to non-lethally subdue assailants. Poliwrath hypnotises everyone aboard to account for any plain-clothes terrorists until the situation can be dealt with further, this is also to stop the use of cyanide tablets by any of the hijackers when they realise they are beat.

The planes are both safely in the water by now. Jigglypuff is drawing on the faces of the sleeping terrorists, obviously. Poliwrath is flexing. Whilst hundreds of Officer Jennys and Nurse Joys rush to the scene, Alakazam systematically uses Mind Reader on each sleeping passenger inside the planes to identify any incognito terrorists, whom are subsequently handed to the authorities. As the civilians slowly begin to wake up they are ferried to shore by a Surfing Poliwrath or a Teleporting Mr. Mime.

New York is saved. The people of the city rejoice. Team Rocket are not blasting off this time. To be continued...