Reskinned Skill List and Athletics Confusion

[sandmote]

The core rules say that a DM usually asks for a Ability+Skill combo, while I prefer to only ask for an ability, and let the player get creative with how his skill applies.

The core rules say the DM asks for an action, and then assigns an Ability + Skill combo to the action the player chose. From your linked source:

Essentially, the idea is that a player’s job is tell you WHAT they want to accomplish and HOW they want to accomplish it. When a player says, “I want to pick the lock,” what they are saying is “I want to open the door BY picking the lock.” Simple, right? But important. Because that’s different from saying “I smash down the door,” which is saying “I want to open the door BY breaking it down.” But it also isn’t. The OUTCOME is the same: the door is open. But the APPROACH is different: how they get the door open.

Based your example (directly below), you're adding an additional step to determine the player's relevant skill, but I don't see what it adds.

Using Skills
In 5e, skills come into play after the DM has asked a player for an ability check, either in response to player intent or an in-game event. When the DM asks you for an ability check, you get a chance to add your proficiency bonus to the check by explaining how applying one of your trained skills might increase your odds of succeeding.

Player: Can I search the body for some valuables?
DM: Sure, make an Intelligence check for me.
Player: I am trained in investigation, can that help me look for hidden pockets other might miss?
DM: Absolutely, you can add your proficiency bonus to the check.

This might work better if you used a less obvious example here. I'm familiar with when Investigation applies to Intelligence checks.

For contrast, if I'm making the player pat someone down to look for hidden pockets, I'd probably make it a Dexterity (Investigation) check, as it combines their ability to recognize which parts of the other person's clothing to feel around in for a secret pocket. Note that because they don't know what they're moving their hands to do I wouldn't use an Intelligence (Slight of Hand) check.

I will, however, admit I use a much larger variety of nonstandard checks, rather than making then rare the way Angry GM describes. In addition to helping the players be creative, it disincentivizes automatically choosing the skills tied to your highest ability score.

I have come up with a campaign-specific skill list, as discussed here, and then created guidelines on how these skills can be applied. My players don't speak english as their first language, so it's important to give examples on where a proficiency bonus can be applied to an ability check, in order for them to understand each skill's niche and how to get creative with it.

I think this is the issue I'm having.

Knowledge, Leadership, and Speechcraft are, I think, the worst offenders. Based on the description, Speechcraft applies to attempts to calm, convince, and trick, while Leadership applies to attempts to calm, convince, trick, and scare. And I've harped on knowledge a lot.

I don't see when "Knowledge" would apply. If a Character is proficient in "History," I can say the bonus applies to heraldry but not marine life. The same goes for a "Knight;" bonus against heraldry but not to marine life. Meanwhile proficiency in "Nature" or as a "Sailor," would know about marine life, but not heraldry.

It's also an issue in the other direction. Someone trained in "History" is likely to know not only about heraldry, but also old nations, major battles, and political actions. A "Knight" meanwhile, would be have a bonus to recognizing heraldry, knowing proper codes of conduct, political maneuvering, and ransom negotiations. I don't think your skills are specific enough to tell me about what they'de give bonuses to.

Similarly, to the above, if remembering "Intimidation," "Deception," and "Persuasion," is a language issue, it might be easier to call them "Scare," "Trick," and Convince," respectively. A "Trader," might know how to convince, but not scare, acting in the same manner

Strength is described as "bodily power, athletic training, and the extent to which you can exert raw physical force." and the athletics skill only representing a small portion of possible uses of that ability "Your Strength (Athletics) check covers difficult situations you encounter while climbing, jumping, or swimming" source

(So swimming isn't a skill, but swimming while something is trying to pull you down is?)

This works the same way walking does. Walking is a best a passive skill, but walking over something extremely narrow or leaping over something can fail. Similarly, swimming is at best passive, but fighting a current would require some skill. Climbing is passive, but you would have to put in effort to resist being knocked off.