Lots of FBOs will do that. If the schmuck provides them with information on who the pilot will be who does the flying. Chances are 'Larry' is already a flight instructor or contract pilot who has worked with the FBO.
- two phonecalls
- two written invoices, one from the FBO for 'aircraft rental', one from the pilot for 'piloting services on x/x/2019
...and all the parties have to be in agreement that schmuck is the operator of the flight who employs the professional services of 'Larry' as the pilot. 'FBO' is only involved as the lessor of the plane. Now as the operator of the flight, schmuck would probably want to carry insurance coverage for his risk exposure, particularly if schmuck does this flight on behalf of 'schmucks general contracting'. But that's what commercial non-owned insurance is for.
If this becomes an ongoing setup in the sense that 'Schmuck' has a standing agreement with the FBO to use the plane with 'Larry' or any other suitably qualified pilot, it can be advisable to submit the lease to the local FSDO for their review. They tend not to like a setup where more than 5 lessees have an ongoing rental on the same aircraft.