Warmaster Horus
Explorer
A general Interaction check would just be a Charisma check in my view. In fact, if instead of calling for a particular skill, you just let the player claim a skill applies to the ability check you do call for, it all works out fine. The player generally knows what he or she was going for when describing what the character is doing, so it does not require the DM to interpret the intent. He or she need only call for the Charisma check and the player takes it from there, adding the appropriate skill. This assumes, of course, the player is acting in good faith with regard to action declaration and applicable skill.
Something like that works. I'm a believer in allowing interesting combos of stat/skill bonuses that add some verve to the narrative. I had a situation a while back where the DM asked me to make a Wisdom/Stealth check because my PC had to remain very still and silent for a prolonged time to avoid detection by a creature with tremor sense. You need to be a bit careful about player abuse of always cherrypicking their best stat-skills and trying to apply them to all circumstances. Or allow them to try but with a higher DC or Disadvantage because it's so outrageous.