What’s the meaning of “He’ll stay their wicked hand”

You are right, it is fine to use "on the other hand" without explicitly mentioning "the one hand" - the reader/listener can easily infer it.

Indeed, using "on the one hand... on the other hand" in most contexts sounds laboured and overwrought. It is sometimes useful to signpost to the audience in advance that you are going to supply an opposing view later, in which case it is useful - but for the most part it is better to leave the first part out.

In support of this: I spent a little time perusing the British National Corpus. It reports 5311 uses of "on the other hand", but only 1417 of "on the one hand". That would seem to suggest that "on the one hand" is only used roughly one third of the time, but in fact it's even less than that, because (judging from a random sample) most uses of "on the one hand" contrast it with "on the other" (or not at all) - so it's probably closer to one in four.

'Not quite a Haiku' is referring to the three short sentences:

He worked the rope line.

Lots of teenagers.

There was more screaming.

It comes close to the rules for Haiku (in English of course) of 5-7-5 syllables and pithy poetic meaning. I think it is obvious that it doesn't match the syllables and also it is not particularly poetic.

I haven't heard the phrase before but it could easily be a common trope. It's not an idiom though: it means what it says, it's just that what it says may not be obvious. It has nothing to do with 'work' or 'hanuatu', just to the form of some description (simple, few points, possible poetic).