Another corroborating proof
Jesus Himself made a prophecy of how He would be impaled:
John 3:14 “And as Moses lifted up the serpent in the wilderness, even so must the Son of Man be lifted up,
Here's the Old Testament verse referred to by Jesus:
Num 21:9 So Moses made a bronze serpent, and put it on a pole; and so it was, if a serpent had bitten anyone, when he looked at the bronze serpent, he lived.
More Bible verses not using cross
Acts 5:30 The God of our fathers raised up Jesus, whom ye slew and hanged on a tree.
1 Pet 2:24 who Himself bore our sins in His own body on the tree, that we, having died to sins, might live for righteousness–by whose stripes you were healed.
Again, according to Strong's Concordance, here's the original Greek word for “tree” used in the above verses:
G3586 ξύλον xulon (xï '-lon) n.
1. wood, timber (as fuel or material, of utility and benefit).
Finally, The Companion Bible concludes:
“There is nothing in the Greek of the New Testament even to imply two pieces of timber.”