My suggestion would be for the players to pre-specify which ability they intend to use by default with a skill, and write the corresponding total down on their character sheet. Silly stuff should be disallowed, but obvious combinations like Strength modifier + Intimidate for example should be fine.
As a DM, I'd be inclined to allow any of the following by default:
- Acrobatics - Dexterity or Strength modifier
- Animal Handling - Charisma or Wisdom modifier
- Arcana - Intelligence or Wisdom modifier
- Athletics - Dexterity or Strength modifier
- Culture - Intelligence of Wisdom modifier
- Deception - Charisma or Intelligence modifier
- Engineering - Intelligence or Wisdom modifier
- History - Intelligence or Wisdom modifier
- Insight - Intelligence or Wisdom modifier
- Intimidate - Charisma or Strength modifier
- Medicine - Intelligence or Wisdom modifier
- Nature - Intelligence or Wisdom modifier
- Perception - Constitution or Wisdom modifier
- Performance - Dexterity or Charisma modifier
- Persuasion - Charisma or Wisdom modifier
- Religion - Intelligence or Wisdom modifier
- Sleight of Hand - Charisma or Dexterity modifier
- Stealth - Constitution or Dexterity modifier
- Survival - Constitution or Wisdom modifier
Specifying this ahead of time, opens up some options for some alternate character builds. You don't necessarily have to have a high Dexterity character to be good at Stealth, you could take advantage of your higher Constitution, your stamina helping you keep your breathing quiet and remaining still.
One of the problems with 5E D&D was that certain abilities were key for skills, particularly Charisma, Dexterity, Intelligence, and Wisdom. There is an advantage of being to write down the skill + ability modifier total to roll with, but that can be achieved while allowing more flexibility as in A5E. I will note that the virtual table top that I use, Fantasy Grounds, while it allows you to switch ability modifier to apply to a skill, has certain defaults, so ideally best to adjust that outside of the main game play to speed things up.