The single-pull work-songs are a bit harder to sort.

There are the short pieces that have customarily been considered as formally too primitive to be chanties -- that is, so far as chanties as we have become accustomed to them are more developed and song-like. But I think that distinction (more or less primitive) is a difficult one to maintain; one is better off just describing the thing as it is.

Hugill appears to lump together under "sing outs" at least two different sorts of action. One is constant, such as when hauling in the slack of a rope, hand over hand, quickly and without any particular need of coordination. Let's disregard that.

The other is a song to coordinate a concerted effort. The bulk of that category consists of chants for "sweating up" / "swigging down" (same thing), which is that practice of throwing the weight of ones body down to get the last few inches of tightness on a line. Such a chant was also used for stiff jerks on tacks/sheets. I have a general understanding of these things, but I'm no pro, nor have I done them myself.

I've created a thread that has attempted samples of just about every documented chant of this type -- so far as Hugill compiled most of them in his SfSS.

sing-outs thread

As the discussion goes there, too, it is dicey business to try to distinguish these from some other songs that have been given the honor (i.e. in collectors' books) as fully-fledged shanties.

Description: The sweating-up chants have short phrases, at the end of which is a refrain. Sometimes --notably-- the chorus joins in only on the last word or two. Most importantly, the moment of action usually occurs at the very end.

I want to use that as a baseline, then, and see how short-hauls that have been called "shanties" are similar or different.

I think "Johnny Bowker" absolutely belongs to the sweating-up category (also used for sheets). One could speculate reasons why it has been handed down as a "major" chantey rather than as a "minor" work chant, but I won't.

"Paddy Doyle" is just like any sweating-up form, it just so happens that it got linked, somehow, to the bunting task. Custom, I suppose.

For tacks/sheets are the following.
"Boney" - could also be for halyards if the pulls are timed differently. Indeed, because of its two often rhyming phrases, it can morph into the classic form.
"Haul Away, Joe" - The only thing that distinguishes this and the following from other sweating up forms, I think, is that the end refrain is a bit longer and the melodies a bit curvier.
"Haul The Bowline"

I don't think "Grog Time of Day" or "Do(odle) Let Me Go" belong to these categories. "Grog" was for rowing, "Doodle" was cited as capstan, and FWIW I think, based on form, that both could work for 2-pulls. In any case, I don't think they belong here.

The next few are HALYARD chanties that have one pull. They have the form of the "classic" halyard chanties, it's just that they are described as having only one pull.   The pull did NOT come at the end, as it would in a sweating up chant or sheet chanty. These are not short haul shanties! However, note the commentary:
"High O Come Roll Me Over." Thought to be originally for log-rolling. Hugill thought it should also be used for tacks/sheets. In that case, the pull would come on a different spot. If you ask me, I'd say that spot should be on "over."
"Hurrah, Sing Fare Ye Well." Just like any halyard chantey IMO, 'cept it has only one pull.
"Tommy's on the Tops'l Yard." "mainly for quick light pulls on the royal halyard" -- hence the one pull, and the probable quick tempo. In Hugill's rendering, the place of the pull varies between the first and second refrain. I am skeptical. Noted that this was also for tacks/sheets.

Although "Cheerly Man" has been put in the halyards category (Dana used it for catting anchor, though), it does not share the form of the preceding three. It really is much more like a sweating-up form, that, for whatever reason, came to be used at halyards. Hugill calls it "just faintly removed from singin' out". Perhaps because it's structure is more complex (stanzaic), it wants to go under the "full chantey" category. However, if you break down each phrase of the stanza, it's just a series of sweatin up chants.

A different form altogether is found in "Dan Dan" and "Ek Dumah." This form has a fast paced, continuous set of single-pulls. I'm not sure if I really need to say more. Just listen to it. There are a lot of pulls, meaning they were not for short jobs, i.e. they could be for longer jobs like halyards (really, I'll bet they originated as some other kind of shore-side work-song).

Sorry, but these don't really fit into a nice list!