Today I had the opportunity to visit the Kotel Katan, a small part of the Western Wall that can be reached only by walking through the labyrith of streets in the Muslim Quarter. At no point did I feel unsafe walking there with my family.
There were two bored Israeli guards watching the area, and absolutely no one else was there. Since it appears that the Kotel Katan is even closer to the Kodesh K'dashim (Holy of Holies) than the main Kotel, this was surprising and puzzling to me.
Here are two shots of the Kotel Ha-Katan:
Right nearby is a small gate that leads to the Temple Mount itself, also guarded by the same guards to not allow Jews to enter. I did manage to snap a shot through the open door: