It would mean that any channeler characters would be either, if female, restricted by the Three Oaths (or if you also have the Wise One / Sea Folk channeler options, no Three Oaths but far more limited possibilities), or, if male, would develop slowly and be prone to uncontrolled outbursts that can harm your own group.
Also, I'd say a separate story that intertwines with the plot of the series but doesn't follow it might be better.
This makes me wonder if anyone ever played the actual WoT video game they made 20 years ago? It definitely wasn't a BG style game, more an action RPG/shooter type game, but I never played it.
To handle the One Power problem, the main character was an Aes Sedai, a full fledged Aes Sedai that held the rank of Keeper mind, that could barely channel a trickle of the One Power(which she likes to point out. A lot.).
Instead she used that trickle to activate ter'angreal. Which basically served the role of a fairly flexible arsenal of guns... Which in and of itself is lore breaking, as thousands of year old ter'angreal that draw power from the OP using "ammo" or being "depleted" after one use is kind of silly. These are relics of a past age we are talking about, not something you can just buy at the market one town over. Yet game WoT is literally swimming in the things.
Then of course, there are things like Whitecloaks actually being willing to use ter'angreal. Literally nameless Forsaken that are somehow free, or a channeling sudo-Fain called the Hound running around... Oh, and speaking of sudo-Fain, weird alien like monsters in Shadar Logoth.