Cyberpunk 2077 was meant to have wall running initially but now it appears that CD Projekt Red ditched this movement mode. It remains to be seen whether Mantis blades can still do something similar.
CD Projekt Red set out to give players as many choices as they could in Cyberpunk 2077, one of them being how to approach different situations and areas. Initially, they showed some wall running in 2018 during the 48-minute gameplay video but that part of the game has since been scrapped.
This was confirmed by Max Pears, Cyberpunk 2077 level designer, in a conversation with Gamereactor . They spoke on the subject of wall running, which was briefly shown before V latched onto a wall with her Mantis blades. You can find that particular scene in the video below, at the 42:55 time stamp.
However, it "is something that [CDPR] removed due to design reasons" according to Pears, although "there's still going to be a lot of flexibility in how you move".
The first part of the sentence is the last nail in wall running's coffin so we are pretty much sure it is not going to appear in the game. On the other hand, both the wording there and the second part of the sentence left out any mentions of Mantis blades.
In short, Pears did not confirm nor deny that traversal options with the blades are still in the game.
Without wall running, using them in such a way might be hard or obsolete but there might be something we are not seeing just yet. The bottom line is that wall running is gone while the future of hanging on the wall with Mantis blades is uncertain.