While I like to improvise I'd never want to use a cut-off cable anywhere near a toddler. Whatever the savings or practical benefits, they just can't outweigh the risk of the toddler doing something that causes a shock, fire, ... Maybe for the best that you removed that light strip.

waiting for the next piece of this story, where your toddler turns 13 and gets their first mp3 player, which doesn't ship with a charger and guess who still has 18 inches of cable left?