Good catch! ;-) My somewhat limited Greek forced me to the lexicon for this one, but apegxato looks like it translates close enough to "choked himself" for my taste. Still, it's a fair inference, again harmonizing the passages, that he choked himself via hanging, as it is both intuitively more efficient and fits better with the necessity of his being over some precipice and falling hard and fast to the ground.
We don't know if it was the hanging or stangulation that killed him or being squashed on the rocks. I suspect the latter since in hanging you don't really die until about 5 minutes after you black out.
The Greek in Acts 1:18, is describing what happened to his body after he hangs himself: [This indeed(Peter speaking of Judas)then got a field out of the reward of unrighteousness, and having headlong fallen burst in midst and gushed out all bowels his.]
So Judas did not buy a field....he instead threw the money back into the temple and went and hanged himself. See also Zechariah 11:12-13. After hanging himself, and his body neglected and ignored by most....it rotted, and fell from the noose and upon hitting the ground, literally burst open in its rotted condition.....and his insides came flowing out. He indirectly bought the field with his efforts.
Choked himself? Ha, little naive -- have you tried that. Hint: you pass out and you stop choking yourself....nice try in linguistics.