You need to submit (fax/email) a completed General Aviation Report form to Special Branch in Northern Ireland, and another one to the Police in the Isle of Man. The one for Northern Ireland needs to be submitted at least 12 hours before the flight, but the Isle of Man one does not require any prior notice.
The UK GAR form is in "Related documents" on the right-hand side of this page:
https://contact-ukba.homeoffice.gov....eral-aviation/
The Isle of Man form, which is different, is here:
Light Aircraft Visitors - Isle of Man Airport Website
There's a web/app-based GAR submission gateway somewhere that's supposed to simplify the submission process, but I've never used it.
Handling is not mandatory on the south side of the airport where Manx Flyers used to be, but you'll probably find it easier, albeit expensive in a "I'll never set foot here again" way, to use the light aircraft handling agents. Their contact details are on the second link above (Rendezvous Handling).
The alternative is to exit through the turnstile taking care to ignore all offers of fuel, cups of tea, mints etc. from the handling agent, and then call a taxi using the number you got off the internet earlier to get you where you want to go. You'll need to arrange for airport security to let you back onto the same apron when you leave. I expect you can get the control tower to send them round when you telephone them to book-out.
Best of luck.