I would....
If talking to a LARS unit and transiting high above - say 4k - then I would remain with the LARS unit.
If NOT talking to anyone, I'd give the airfield a shout...Same as if passing abeam < 10 miles, I'd give them a call.
I'd also have read the Notams and avoid any airfields with notams for stuff in the overhead or any with a parachute symbol
