Yeah, the wrist/hand/body tape was as a result of this scene, which is not in the final cut of the film...for some reason. After he gets his hands and body cut by Funboy, he puts on the black electrical tape.
https://www.youtube.com/watch?v=cwGpJr0PALE
Yeah, weird they cut that. But even so, its the 'some reason' part I've always found odd.
In the comic (though its never said outright) it appears to be that self inflicted wounds either don't heal or not as well. While grieving he starts slashing his own arms and wrists then tapes himself up to stop the bleeding.
In the film? How are those wounds different from everything else? They'd heal fine on their own.