I did not know that, I always assumed the Mummy in that film had a different name. Shame on me for not watching it then, I'll do that tonight. Though the idea of having two different figures of Kharis is appealing if I'll be honest.
While I adore (border line mania) the Universal Monsters flicks, Hammer's original 1959 The Mummy is a masterpiece. It is my favorite Mummy film of all time. The colour, direction, soundtrack, Lee and Cushing, and the fact that they took all of the elements of Universal's 1940's series, and made it into a rather neat and cohesive plot, is sresponsible for my adoration of it.
Lee hated the role because it caused him injury on set. So he was loathe to speak highly of it until he was a little older. Then he changed his tune. He considered it a masterpiece.
Lee dislocated his shoulder busting through a set of glass doors that were supposed to be unlocked....and weren't. So when he barrels through,....it's real! He was pretty strong.
There is also a scene where they literally blow a hole or two in the Mummy's wraps, and the effects burned him.
In a production still, his neck wrap is seen unsnapping, as he was very physical in the role.
So he wasn't thrilled about doing it. Yet, as stated, years later he warmed up to it and called it out for its brilliance.
In later Hammer Mummy entries, there are different mummies who are NOT Kharis that are featured. That's probably why you didn't remember Hammer having a Kharis.
I have devoted a great deal of time to the watching and rewatching of these films. Those were the days.