Wetzel played lead trumpet for Woody Herman from 1943 to 1945 and for Stan Kenton from 1945 to 1948. He recorded in 1947 with the Metronome All-Stars, Vido Musso, and Neal Hefti, and married bass player Bonnie Addleman in 1949. While with the Charlie Barnet Orchestra in 1949, he played trumpet alongside Maynard Ferguson, Doc Severinsen, and Rolf Ericson. He played with his wife in Tommy Dorsey's ensemble in 1950 and with Kenton again in 1951. While touring with Dorsey in 1951, he was killed in a car crash at the age of 27. He never recorded as a leader.
He is credited with composing the Stan Kenton tune 'Intermission Riff'.