Skills are not hard-coded to any ability (see the "Using Ability Scores" portion of the basic rules). The ability that appears beside them and in their descriptions is only the most common. For example: Intimidation is most often used with Charisma. But given certain situations, like a strongman crushing a rock with his bare hands to intimidate, that would make sense as an Intimidation (Strength) check, or in a trial a smart character could try to intimidate a member of the jury slipping certain details in his speech that let him know that you are unto him, that would probably be an Intimidate (Intelligence) check.
In total, if you allow Arcana (Wisdom) or Arcana (Charisma) checks the variance would be of just two or three points in a d20 roll. It would be noticed, yes, but nothing too wild.
Your solution might not be needed.
Not all magical knowledge falls under the Arcana skill. You can use Religion for divine spells from Clerics or Paladins, and Nature for spells from Druids and Rangers. And since you can attribute any Ability to any Skill as long as it fits, all of those could use Religion (Wisdom) or Nature (Wisdom) for their spell know-how, arguing that they operate their spells more from "instinct" than "intelligence".
This means that to know what a Druid is casting, your Wizard might need to do probably a Nature (Intelligence) check, as he does operate via intelligence, but the knowledge he is trying to figure out is not Arcane at all, but natural. But this is not RAW nor RAI so take it just as a flavorful suggestion.
This has another reason to be, and that's balance. Other than your magical know-how, every knowledge skill has different areas of expertise.
Arcana. Your Intelligence (Arcana) check measures your ability to recall lore about Spells, Magic Items, eldritch symbols, magical traditions, The Planes of Existence, and the inhabitants of those planes.
Nature. Your Intelligence (Nature) check measures your ability to recall lore about terrain, Plants and animals, the weather, and natural cycles.
Religion. Your Intelligence (Religion) check measures your ability to recall lore about deities, rites and prayers, religious hierarchies, holy symbols, and the practices of secret cults.
Note that every single one of these let's you know completely different things. Like with Nature you would be able to know details about any beast or plant-like monster, or with Religion you would be able to know details about Fiends and Celestials and other godly/ungodly servants, or Arcana would let you know how to get to the Fire Plane or weaknesses of a Shadowfell monster.
If you encourage your players to spread their knowledge abilities they gain a lot of coverage, instead of concentrating everything on Arcana.