Perhaps ...
Sell the live bird to the person then get them to ask you to neck it for them as a personal favour , you could also pluck as a personal favour , by hanging it from a frame or having it across your knee .
The deed of drawing the bird can be as a personal favour and can be done on a sheet of wriggly tin covered in a food grade plastic sacks or aprons .
If I recall it correctly that's how loads muslims got round the clean slaughter angle for sheep and goats .......because they had already purchased the animal , with a date & time given on the reciept.
They didnt need a slaughtermans licence either just an islamic priest to say some prayers .
The laws might have changed but it may be worth while investigating .. just don't ask the jobs worths for one of them will be honour bound to say No you can't do it.