Someplace I have a National Geographic from 1943 and there is an ad (think it's a Boeing ad) which has a picture of the Swoose in Australia taken in 1942 and I want to say that the it was in the OD/Black scheme. I think its in storage but will check.
The Smithsonian web site does not say what color the aircraft was painted in upon its return to the US. However it indicates that by mid 1944 the a/c was silver and based in Panama. At that time it was rebuilt, with the belly tub and astro dome above and behind the pilots removed and the nosecone was replaced with a nosecone from a B-17F. At the end of the war the plane was shipped to Kingman for disposal and eventually purchased by the city of Los Angeles for $350. During the preparation for the move to LA, the aircraft was "repainted" in the OD/black paint scheme. When the city's plans for the aircraft fell through, the aircraft was donated to the Smithsonian, where the aircraft remains with the modifications and paint job.
I could be pretty wrong, but as the spark plug behind the movement to save the Swoose, that Col Kurtz (the Swoose's origional pilot) would probably have wanted it painted in the scheme that it carried when he flew it in combat. Just a thought.