Instead of modifying the wires by cutting, have you thought of maybe just bundling the excess wiring neatly into a loop or small bundle and wiretying them using plastic tie wraps? I do this all the time; you'd be amazed at how neat it can look without any cutting, splicing, etc.
You should be able to cut the wires if you really want to but I would solder the new connections and use plastic heat shrink tubing to cover the bare wire joints (I would NOT use tape). The best way, however, would be to buy new pins/connectors. Once you cut the wires to the length that you desire, then you would just attach the new pins to each of the wires and insert the pins into your new connectors. Most electronics stores should stock these pin/connector kits. Since there are several wires, this will be a tad tedious (use tape and mark each wire and it's location) and you would want to make absolutely sure that you put each pin/wire into it's exact location or else you will damage your mobo! You should be able to use a small jewelers screw driver to remove each of the pins. You will probably have to solder each pin to the wire although I have seen the type that crimp using needle nose pliers or a crimping tool.