Check to see whether your webcam pcb is usb (if it has four wires, red green black and white then it probably is usb). Try soldering wires of the same colours to a cut-off usb cable and plug it in to see if it works. If it does, great, otherwise you could try swapping wires (for some reason I've found usb cables with non-standard colours.)

Print (I used slic3rs support option, with 5mm spacing which worked very well)

I used hot glue to attach the board to the recess on the back, then soldered the wires in the small groove on the print. I hotglued the cable to the back of the case as stress-relief. I glued some thin strips of inner tube to the inside for grip, though this was probably not necessary/other rubbery things would work too.