That shows the proper way to pull a hub cover, but the pics show the non wire side. Same procedure on the wire side, but a bit slower and easy, as you make sure the wire feeds through the notch cleanly.
If the wire was damaged, and a crapton of tape, shrink or other stuff is on it, you have to carefully remove that so the wire will again fit through the notch. Once the bearing is off the axle shoulder, there should be additional room for you to feed that wire past the part of the axle without the notch.
Its possible to pop the cover off with three screwdrivers, leaving the core in the hub. Again, slow and careful so you don't damage it. If you ever expect to do this again, the three jaw puller is worth every cent. Some car parts stores will lend you one for free, with a deposit on it.
You can start by pushing on the wire side axle with the puller, this will pop the cover down the axle. then when the puller is removed, the magnets will pull the core back into the center, and the cover will then pop. Sometimes you may need to use a knife to start it, because its silicone glued on. Once popped, the cover can usually worked off carefully by hand, or use the puller on just the cover.
The method I don't advise, is the slam it on the table technique.