If you are talking about removing extra connectors daisy chained to a PSU cable (example: you have a SATA power cable that has four connectors on it and you only need one or two), removing a pin so you can snip off the extra wire close to the pin where it won't show, then reinserting the pin into the connector is a doable option. However, removing pins without damaging them, even with the proper tools, isn't always as easy as the videos would have you believe. You could just snip the extra wire flush to the connector and carefully put a drop of liquid tape or RTV on the exposed copper to insulate it. It wouldn't be quite as sanitary looking but you don't have to worry about ruining pins that way.
Removing extra cables is another story. You could cut them off close to the PSU and put a length of heat shrink on the end to insulate them but that would leave an ugly stump by the PSU. You might even be able to open up the power supply and snip the cable close enough to the PCB to not need to worry about insulating the remaining end. Then you wouldn't have the ugly stump. Either way, however, you would never be able to use that cable again. Another way would be to snip the cable off at the first connector and insulate the ends (of course, this wouldn't work on an extra MOBO ATX power cable since it's a long cable with only one connector on the end). Even though it would leave a longer length of cable coming out of the PSU, it would be easier to hide, especially if you bundled the unused cables together to appear as one, massive cable. You could always replace the removed connectors and cable in the future by crimping on new pins.
Keep in mind, replacing those removed connectors and cables will be even harder to replace than removing them, should you ever need them. Any warranty on the PSU will be voided. You also run the risk of ruining your PSU, possibly taking out other components. Of course, ruining a PSU would give you the opportunity to buy a new, modular PSU. You could even make custom cables for it (cautionary note: making custom cables dramatically increases your chances of releasing the built in smoke from a PSU and other components).