If you do the checkride in a 737 sim the ride would be for both the ATP-ME and 737 type. Because the ride is being done in a sim it falls under part 142 and that requires an approved training program of both ground school and flight training. The 737 type is probably the most common type in the US and many training centers offer it. Because you have time in the aircraft you should qualify for a reduced training program.
The other option if you don't need the type on your FAA cert is to thrash around in a Baron or 310.