Can you use shoe polish to change the color of an extension cord?

Shoe polish will likely stain things that touch it -

or it will flake off and and leave clumps around your home. You’ll hate it! You would have better success with a spray paint made for plastics. :)

I would be more apt to use a permanent marker, lots of color choices and shouldn't rub off.

I would spray paint it.

plastic spray paint would be better probably. Although I have used furniture polish for other things including plastic and it did just fine....like a permanent marker. It probably would work, but the question would be how long would it take to cure and if it is left on a rug, would it eventually stain it? I am assuming this is for indoor use?

I ran across this: https://makezine.com/projects/cable-dyeing/

I agree with the permanent marker idea. But spray paint would be a close second. But a no on the shoe polish if you are looking for a somewhat permanent solution.

I would say spray paint would be better

Is it rubber? If so, spray paint won't stick. I wrapped a cord in twine which you can see here: https://www.flippingtheflip.com/2014/04/nagging-projects-day.html

What kind of glue do you use that peels off of your fingernails?