Can I cut down a quick release skewer?

You can cut the skewer, but be sure to leave enough thread on there to keep the nut on when the QR is opened enough to take it off your bike (without having to remove the nut).

Don't forget to file the sharp cut edge smooth afterwards.

Yes, in fact you should cut it down because it's both a safety hazard (easy to gouge your ankles on an exposed bolt) as well as maintenance issue (it's easy to bend the exposed axle bolt and thus make it very difficult to unscrew the QR nut).

There are two ways to cut it, the first is on the bike and the second is off the bike.

On the bike:

1. Keep the wheel on the bike and use a hacksaw to gently cut through the exposed bolt. If you don't want to scratch your QR nut, you can protect it with some electrical tape.

2. After you cut the bolt off unscrew the QR nut, this will clean the threads. Use a file to clean up the end of the bolt as it will have sharp jaggies.

Off the bike:

1. Before taking it off the wheel, use a magic marker to mark on the bolt where it meets the face of the nut.
2. Unscrew the nut and remove the axle bolt from the wheel and put it in a vice.
3. Screw the QR nut back on (or use equivalent size real nuts) so that you can use it to chase the threads.
4. Cut the bolt at the right place using a hacksaw or dremel
5. File down the jaggies.
6. Use the previously screwed-on nuts to chase the threads.

Success!