I often see two-handed used with weapons. But have never seen two-hand.
However, with a weapon that needs only one hand I've met both one-hand and one-handed.
Are they both correct?
"Hand" and "handed" have two distinct meanings.
You can describe a weapon as "a one-hand weapon" or "a one-handed weapon" because the first describes the design of the weapon (it fits in one hand) and the second describes the way that it is used (it can be fired with one hand).
You can't say "two hand" in the same way, because it would be "two hands". And I would suggest this is why you do not hear a weapon, or anything else correctly described that way.
Definition of one–handed MWD
1 : having or using only one hand could beat him up one–handed
2 a : designed for or requiring the use of only one hand
2 b : effected by the use of only one hand
So it is defined in the dictionary. I've heard "He caught it one-handed."