I would say that the signature "Two desperate men" actually has two separate meanings. Remember, Bill and Sam have kidnapped Johnny in order to extract a ransom from the boy's father. Therefore, this signature should be understood as conveying a threat, as to the lengths the kidnappers might go to should Johnny's father not submit to their demands.

However, O. Henry's story is shaped by a fundamental irony, and this irony manifests within the signature as well: it is the kidnappers who are terrorized by their victim, rather than the other way around. Handling Johnny is far beyond the kidnappers' abilities, and the boy's father seems to anticipate this. He responds by calling their bluff, demanding that the kidnappers pay him a ransom, rather than the other way around. Thus, the story's resolution reveals just how desperate the two kidnappers are, albeit in a spirit very different than the one they had originally meant to invoke.