DubbaC,
as Hindemith emigrated to the US in 1940 and taught at Yale, you will probably find quite a bit there. You may also want to write Schott (the publisher) for more information (
http://www.schott-music.com).
There is plenty of stuff in German on the net but that probably does not help you much!
Here are a couple of links in english that I have collected over time:
allmusic ((( Sonata for trumpet & piano > Description ))) Sonata for Trumpet and Piano
I found this quote at Tom Stevens Website:
"Updated Supplemental Miscellaneous Intelligence: The use of the clarinet for the performance of a trumpet sonata was not unique at the time. On the inside title page of the original published version of the Paul Hindemith trumpet Sonata (Edition Schott 3643, Germany, 1940) there is a note, written in German and followed by the initials P.H., stating that a Bb Clarinet or some other high instrument, such as an Oboe, Violin, or Viola, could be used in place of the trumpet for the performance of the piece."
Hindemith Sonate