Maybe you have to have a url to the image, but you could just upload it to imgur und copy the link there. You can replace the icon url by searching for “apple-touch-icon” and changing the href property everywhere you see it to the image url.

Say you want to use this icon: https://i.imgur.com/kUxXoIA.png

You change this:

<link rel="apple-touch-icon" type="image/png" sizes="180x180" href="/favicons/apple-touch-icon-180.png">

to this:

<link rel="apple-touch-icon" type="image/png" sizes="180x180" href="https://i.imgur.com/kUxXoIA.png">

(and repeat this everywhere you see the “apple-touch-icon”)