The objective measurement for "skill" is how much training/experience/talent is required to carry out a particular job. Sure, there might be some fuzziness/ambiguity to this, and there's various degrees of freedom to how you compute a "skill score" or whatever (eg. what's more skilled an accountant or an auditor?), but it's hard to argue that a burger flipper is more skilled than an accountant. You can make the argument that the value of a burger flipper vs an accountant is subjective, but that's irrespective of the skill required.

Whether someone is getting "underpaid" or a "fair wage" on the other hand is entirely subjective, and you can come to whatever conclusion you want depending on your politics. On one side of the spectrum you could argue any sort of situation where the employer is capturing surplus value from the employee is inherently exploitative[1] and therefore "underpaid" and a "unfair wage". On the other end of the spectrum you argue that supply and demand curves are the ultimate arbiter of what's "fair", and any wage that is determined by the free market can't by "underpaid" or "unfair" by definition.

[1] https://en.wikipedia.org/wiki/Labor_theory_of_value