I'm not sure how well this would work in your case*, but I've got a script (not originally by me) which "compiles" a web page and its assets to a single HTML file with data URLs. It might be possible to use this script to convert the files that Edge spits out into a single page, then you wont have to worry about extra files getting deleted.
I mainly use it for converting s5 presentations to a single file for easier sharing/portability, and it's always worked for that.
It's a bit of a faff to set up - you need to download the dependencies listed in the doc block and put them at the relative locations shown by the require statements (or change the require statements).
*Taking a look, if Edge embeds assets with tags other than img, link, object or script (e.g. audio, video, embed), you'll need to add them to the $selectors array near the top of the script.