You could test it to see.ĮDIT: I just watched some of VisionOfNine's run. Its a straighter path to the doorway but I'm not sure if the wallrun will cost you more time than its worth. By the way right at the start of your segment you can wallrun to the higher walkway on the left from the right hand one (The right hand walkway being the one you get to at 1.00 in your video). At least the longer pillar slow mo scene at the end of the segment will be cancelled if you do this. It may or may not be faster, you could do a test with it to see. The downside is because you are jumping off the pillar so you'll initiate the slow mo scene, but you can cancel it by switching to overview and then back again quickly.

If you jump onto the last one and straight to the ledge you'll be forced under the statues head which is a bit further along than where you would start. Also the bit where you have to walk along the ledges (2.40 on your video) before there are some pillars straight in front of you. I take it you know about getting the dagger of time early and how to get the other 2 swords early? Also In your your test run there is a way to cancel the slow motion scenes by hitting the button that gives you a look of the entire area (overview mode I think its called) and switching back again quickly. Its about time someone made a new run of this.

Prince of persia sand of time block