The film's director, Simon Kinsberg has explicitly confirmed that it's Mystique at the end, impersonating Stryer;
Q. WHY IS MYSTIQUE PLAYING STRYKER AT THE END OF THE FILM?
Kinsberg : “I wanted Wolverine to end up with Stryker at the end of the film, but
when we got down the line on that, it felt like such a downer ending,
and there wasn’t any ripple in time. It was the same – the location
where Stryker grabbed Logan was different, but Logan’s fate was very
much the same. I felt like we hadn’t made enough of a ripple.
“So from there we thought about who else it could be. I was thinking
of having other people on the boat – he could be fished out by Charles
and Hank – but we set this thing up where Mystique is masquerading as
a military character saving mutants from going into some sort of
experimental programme in Saigon early on, so there’s a really nice
symmetry there at the end.”
And in this interview with ScifiNow
It’s a neat little handwave, because there’s still loads of things we
don’t know – like how Logan ended up in the Weapon-X project and got
his Adamantium skeleton if he was being led away by
Mystique-as-Stryker and not Stryker himself.