While I agree it would work...
My hesitation to use spray paint would be if you goof up and put too much on, it's a paint to scrape it clean and start over... as scraping just a little off would be exceptionally difficult...
A thin piece of cloth is very cheap... you probably have an old T shirt you could cut up and use... plus it's very versatile that you can double it, triple it, then go back to double, change it out for a different color to give it a colored hue... all with minimal investment and minimal effort...