Does ATC handle non-regular widebody flights differently?
No, ATC does not handle these flights differently from regularly scheduled ops
ATC isn't concerned with why an airplane wants to go to an airport or whether they regularly operate there or even if there are ground services available for them at the destination.
Whether the flight is regularly scheduled or not may fall under different regulations but ATC services do not vary.  The charter flight will be operated under instrument flight rules (IFR) and will have a flight plan filed with ATC prior to departure.  The controllers at the departure airport will receive information about the flight prior to that planes departure and will service the flight to its filed destination.  This works exactly the same way as normal scheduled service by that same (or any other) airline.