Thinking about it, it wouldn't actualy be all that difficult to retroactively reveal that the Weapon X programm existed in the MCU too.
We allready had the reveal that further attempts at recreating and even improving the super soldier serum were made after Captain America (Winter Soldier, Civil War, Falcon and the Wintersoldier) in addition to the experiments which resulted in Quicksilver and Scarlet Witch.
So would it suprise any casual viewer that someone in the past tried a different approach to create such individuals, like gathering rare people with natural super powers, experiment on them to improve said powers and then brainwash them into obedience.
Infact besides Wolverine himself, many casual Marvel fans might also draw comparison to the experiments which created Deadpool in his first movie, which in turn allready feels like an indirect bridge between the FoX-Men and the MCU. So there is plenty of familarity to draw from.
I would also find it a nice twist if it's revealed that MCU logan started out with nothing but a lower end healing factor (extremely slowed aging and the ability to recover from deadly gunshots wounds within days, rather than seconds), surviving the various wars he fought in not because he could just shrug off any injury thanks to healing, but actualy because he was a tough SOB who drew from decades of survival experience in addition to having that slight edge. While all the flashy things like his fast healing factor, super senses and claws actualy being the result of Weapon X modification.
Weapon X could also be the origins of a handfull of other mutants who allready were retroactively present in the MCU, but with the trauma from said experiments having convinced them to either lay low or not bother trying to protect humanity.
Like drawing inspiration from Wolverine and the X-men cartoon, by having MCU Mystique be a Weapon X survivor (and with that knowing Logan) who now impersonates Sharon Carter as the Power Brocker (while keeping the real one imprisoned).
The Power Brocker in turn could also be a nice little backdoor to introduce mutant characters as henchmen without revealing them to be mutants yet. Since after Falcon and the Winter Soldier, the viewer are aware that she ordered the creation of a new super soldier serum. So having more powered henchmen as mercenaries could at first be attributed to that before the big X-gene reveal.