Don't need to wire to the fuse box, you can grab power from the back of the lighter socket, I'm assuming it has one yeah?
Back of the radio is another place that's common to pull accessory power from, see an auto elec or car radio installer if you're not confident on what you're doing there, hard wiring it is really only needed if you want it there all the time, if you might want to use it more often but not permanently you could always just wire a cig plug to the leads (check polarity though as the screen may not have any built in reverse polarity protection), cig plugs are tip positive, outer is earth