Edit re-read your issue, if you aren't happy to find/edit the SQL database for the file in question, you could always just add an adblock rule against it, and manually run your own script from console/greasemonkey it in.
Answer to question in the title:
HTML5 has a feature called an "application cache" just for this. It involves adding a manifest attribute to your <html>
tag.
<html manifest="what_to_cache.appcache">
Then in what_to_cache.appcache
,
CACHE MANIFEST
http://...production.../js/map.js
Future requests of items listed in the manifest will thereafter be loaded from the cache, if available, even if the user is offline. The file is stored in an SQL database for that website, so you can thereafter edit the database.