Does ShortPixel change the URLs of my images?

No, ShortPixel Image Optimizer only optimizes the images on your site, it doesn't change the URLs.

What it can do, though, is to change the markup of your page source code, only if you choose this option (located on Settings > ShortPixel > Advanced):

hat makes the plugin offer URLs for the WebP images so they can be used by WebP-aware browsers, but that doesn't mean the URLs of your current images will be changed.