Travel from Manchester Airport to Sedbergh

Yup ,I would go the airport to Oxenholme
Just put that thru split ticket app and there's direct services and advance tickets can be had from £6.50 ,but £20 ish is more common

There's limited buses from 3 operators from Oxenholme up to " Sebber" as locals pronounce it,
About 35 mins in the bus.
There would be no difficulty getting a taxi if that's your presence ,busy little station

You'd need to take a train from the airport to Oxenholme Lake District station

https://www.nationalrail.co.uk/

then either a taxi to Sedbergh

or there's an infrequent bus

http://woofsofsedbergh.co.uk/?Service_Bus_Times