I have been planning the LED under the slide project but haven't done it yet. My thought was to just route the wire straight up through the slide floor and find a 12v source to tap within the slide room itself. The wires will have very minimal exposure and will never need to move. In the big slide 12v is available behind the outside radio for example. The bedroom slide will probably be a little tougher but there is 12v behind the TV I believe.
Fuses protect the wire and should be sized no larger than what is safe for the wire gauge and length. If you do end up installing a wire that moves in and out with the slide, use marine grade, it is finely stranded and therefore highly flexible and resistant to breakage, plus the jacket and insulation are usually tougher and available in round or flat double sheathed configurations.