Conventionally, it is "He will be hanged."
The etymology of to hang is complex, This is an edited version from OED:
Etymology: The history of this word involves that of two Old English and one Old Norse verb; viz.
(1) the Old English strong hón, heng, hangen, (hǫngen), transitive;
(2) the Old English weak hangian , hangode , -od, (also hǫng-), intransitive […]
In the 13–15th centuries while the south had present tense hang, hong, and past heng, hing, the north had conversely present heng, hing, past hang, hong.
Finally the northern inflection hing, hang was completed by the past participle hung which in the 16th century penetrated into general English.
The weak inflection hanged however continued in use (being the only one used in Bible versions) [and judges pronouncing sentence of death] but was gradually superseded by hung in the general sense, transitive and intransitive, leaving hanged only in the special transitive sense (3) ‘put to death by hanging’, owing probably to the retention of this archaic form by judges in pronouncing capital sentences.
The distinction is found already in Shakespeare, and is established in the expressions ‘I'll be hanged if I do’, and the like.
So basically we have a strong verb and a weak verb. The Bible and Shakespeare went for the weak form to signify a means of death and the strong form for hanging things from other things.
As the Bible and Shakespeare are arguably the greatest influences on the development of Modern English, this is the way things are.
In McMurtry's Streets of Laredo, he uses, Going to be hung
As good as the song is, it is not a reliable authority on the use of English.