10 Theories How Wolverine Can Fit Into X-Men: Apocalypse
9. Stryker's Still Behind It In This New Timeline
What's more likely than Mystique going full mad scientist is that Stryker simply reclaimed his identity and started the Weapon X program himself - unless she removed him from the picture permanently, a high-ranking military official isn't going to take mutant impersonation lightly. This would lead to a situation rather similar to the original X-2 timeline, something we know Singer is trying to use as a baseline.
I wouldn't rule out Raven using him as a cover though, just to tie into Days Of Future Past's ending, but the more anti-mutant stuff needs a vengeful human to be behind it. It's not like the character isn't set up this way either - mutants being held at Alkali Lake isn't far off what he was doing in Days Of Future Past with the Vietnam mutants.
There'd be a nice inevitability element to this, with Stryker getting his claws into Wolverine in any timeline, which also ties into the suggestions from Singer about Jean's emergent Phoenix powers; the canon is different, but certain events still happen.