Can I direct wire a light with a fused plug?
You need to learn the marvelous world of low voltage LED strips

Seriously.  You get a common 12 volt UL-listed power supply, and a small junction box to splice, and the world is your oyster.  

The strips price out at about $7 for 16 feet no kidding.  Not $7/foot, more like 43 cents a foot.  

Since you're working entirely in low voltage, you're at basically nil risk of shocking anyone or setting anything on fire.  The installation rules are also VERY relaxed, and there's no problem doing what you want the way you plan to.  

Which you cannot do with 120V stuff, by the way.