Suicide is indeed used as a verb:
Her husband suicided three years ago. Just like a man!—Lucy Maud Montgomery, 1917, Anne's House of Dreams
Seems a lady poet suicided at Verringer's ranch in Sepulveda canyon one time.—Raymond Chandler, 1953, The Long Goodbye
It is though less common than "commit suicide". And neither would be likely as direct substitutes for "and killed himself" here. The "and killed himself" in the original is a causal use of and; he shot himself and the consequence of that was that he killed himself. Both suicide and "commit suicide" cover the precipitating motivation as well as the action, so it doesn't come after the shooting.
"…suicided by shooting himself…" is about the closest you'll get in rephrasing, and the total number of words is hence the same.