The problem with defining a job as skilled or unskilled is its just an arbitrary definition with no formal ranking.
There are practically no jobs that need no skills. H&S, food safety etc have pretty much changed that in roles you could historically argue had no remarkable skills, say a sandwich maker, they now need to food hygiene training so they are above the average person in this regard.
Cutting cabbages has skills, being able to do it quickly and "safely" (defining safely as not removing ones own digits) are the skills. They are pretty darn specific and pretty darn narrow.
Compare to many professions
When comparing many of the "unskilled" jobs to "skilled jobs" what people are really measuring is breadth of skills, amount of detailed knowledge, transferability of skills etc
Jobs that were historically deemed skilled would often have significant study time to learn the "trade", would have quite a few skills involved in being able to fullfil that role, and that many of the skills would be easily transferrable to similar but unrelated jobs
Going back to our cabbage cutter, the study time is insignificant, the breadth of skills is narrow, the transferability is low. This is very clearly a low skilled job
Driving an HGV, requires some, but less knowledge than say an electrician in study, has a fairly narrow set of skills both physically and from a road knowledge perspective only a little higher than a normal driver, and some but not great transferable skills, most would only relate to other similar "driving" jobs
Take an engineer, high levels of formal training, a relatively narrow set of skills in the field even though they are very complicated, with some skills outside the core in order to be able to do the job well, such as negotiation and presentation skills etc, as far as transferability, again quite high to similar jobs on the technical side, but also quite dissimilar jobs on the softer skills, the negotiation, presentation etc.
One example of a methodology of ranking jobs is the Hay rating. Its still somewhat arbitrary in ways, but at least its formalised so roles compared that have broadly the same rating have broadly a similar mixture of factors.
11. The three elements, Know-How, Problem Solving and Accountability are broken down into the following sub-elements. ! KNOW-HOW - Depth and Breadth of Technical Know-How - Planning, Organising and Controlling - Communication / Influencing ! PROBLEM SOLVING - Thinking Environment - Thinking Challenge ! ACCOUNTABILITY - Freedom to Act - Area and Nature of impact. 12. Each job is measured against these three elements. A numerical score for each is calculated against standard charts provided by the Hay Group. There are two additional elements measured which may be present in some, but not all, jobs. These are: ! PHYSICAL EFFORT - This measures the additional effort or strength involved in performing the job which would be in excess of that expected in a day-to-day office environment. ! WORKING ENVIRONMENT - This measures any uncomfortable working conditions, which would be in excess of that expected in a day-to-day office environment.