Klezmer could have had some influence in the northeast on Jazz since the essence of klezmer is improvisation on the melody line by the lead instruments. Very early klezmer featured the violin rather than the clarinet.
According to the books I have read, Benny Goodman never played klezmer or if he did, its effects were minimal. There is little or no klezmer influence evident in his chops. The only "klezmer" musician in his band was Ziggy Elman. He "played a little Jewish" and wrote "And The Angles Sing" using an old freylach (dance tune) as the melody; a very nice amalgam of klezmer and jazz.

troll