It's pretty fucking clear that that's what happened.
Im not sure about this either. Have to rewatch this particular scene, but to me it looked like he was just still drenched from the rain - looked the same as when he entered Sophies apartment. That hall walk was a pretty dark scene and maybe I just didnt see it, but I always thought he didnt kill Sophie, just like he didnt kill Gary. They havent done him any wrong, hence he let them live.
That's what I thought too. I don't remember seeing him with blood, but maybe I just missed it.