This is a meta-conversation my group recently had. What it came down to was one person pointing out the "skill checks" don't really exist in 5e. Instead, everything is an ability check. First you determine the ability, then you ask if the character has something like a skill or tool proficiency that allows them to add their proficiency bonus, then you roll the dice. A skill check is just a shorthand for rolling one of the most common default ability/skill proficiency combinations. It doesn't limit what the DM can ask for or the players can suggest.
For example, in our game this week our group were investigating an urban worksite that people had disappeared from. I asked the DM if my character could roll Wis + Stealth to look at the problem from the other end and deduce "How would I sneak people out of here if I were trying to make them vanish?" He allowed it and a good roll got us pointed at the possibility of secret passages, which helped other PCs who were investigating the work equipment narrow their search.
So start with the ability. Ask yourself if there's a non-standard skill or tool that might apply. Ask the player in question if they have a proficiency they can justify using in the situation. And if there's really nothing, which should be fairly rare, then just roll a raw ability check.