Harzel
Adventurer
If the core issue is "players have no idea what to do with their skills if they are not specific", then I wouldn't change the rules at all and instead simply give them a handout that lists each official D&D 5e skill with a list of things you can do with that skill.
This. And perhaps to do that in a way that leverages / integrates with how the OP has been thinking about the problem: go ahead and create and/or steal a more detailed list of skills. Then just figure out which 5e skill subsumes each one and use that (along with abilities/skills info from the PHB) to construct the list that @Rya.Reisender suggests. Seems like that would produce a set of ideas for the players that is as specific and suggestive as an expanded skill list would be without the trouble of having to muck about with rules changes.
I have another point to make, but I want to preface it by saying I intend no disrespect to @twofalls or your players - please don't take this comment in a way that is as extreme or dismissive as it may at first sound. Anyway, here's the thing: 5e skills are not meant as buttons to be pushed. The basic outlook for the player should be that the PC "can attempt anything". In the main, ideas for PC actions should arise from their circumstances, not from a preexisting list of things they can do.* Of course, it is reasonable that that should be tempered by knowing what each PC is good at, but in 5e that description by design comprises very general categories, not specific actions. The advantage of this is adaptability to varying circumstances. (The PHB section Chapter 7 Using Ability Scores >> Skills >> Variant: Skills with Different Abilities suggests one facet of this flexibility.)
Now, really, I expect that you understand this pretty well already and so it is possible that I am just a noisy intrusion. But several of your comments indicate, to me at least, that your players are leaning, perhaps oh so slightly, in the direction of wanting to have buttons to push. So I guess the suggestion is that, in addition to supplying the above-mentioned list, focus the players back on immersing themselves in the situation you describe, and understanding that (magic aside) they can attempt anything that would be physically possible (for a hero!) in that situation. If they want to know whether their abilities or skills will give them a leg up (so to speak) on a particular action, IMO there's nothing wrong with having that meta-discussion (as long as it doesn't turn into a lengthy debate).
* This is more or less a restatement of what other posters have already said; I hope different words will be additionally useful.
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