Are you intending the use the AirlineFlightSchedules call or other calls?
For AirlineFlightSchedules, the good news is that you can request data by IATA airport code. That way you can sort of build your ICAO-IATA mappings, or just keep using the IATA you requested.
For example here I request schedules for Charles de Gaulle:
https://flightxml.flightaware.com/json/FlightXML2/AirlineFlightSchedules?startDate=1455206406&endDate=1455306406&origin=CDG&howMany=3
result:
{"AirlineFlightSchedulesResult":{"next_offset":3,"data":{"ident":"BAW8097","actual_ident":"VLG8245","departuretime":1455217200,"arrivaltime":1455223200,"origin":"LFPG","destination":"LEBL","aircrafttype":"A320","meal_service":"","seats_cabin_first":0,"seats_cabin_business":0,"seats_cabin_coach":0},{"ident":"IBE5243","actual_ident":"VLG8245","departuretime":1455217200,"arrivaltime":1455223200,"origin":"LFPG","destination":"LEBL","aircrafttype":"","meal_service":"","seats_cabin_first":0,"seats_cabin_business":0,"seats_cabin_coach":0},{"ident":"JAI6766","actual_ident":"AFR1448","departuretime":1455220500,"arrivaltime":1455226500,"origin":"LFPG","destination":"LEBL","aircrafttype":"A321","meal_service":"","seats_cabin_first":0,"seats_cabin_business":0,"seats_cabin_coach":0}]}}
Does this help?