I don’t have Safari installed so can’t reply to the original question…
Also, I don’t see a link to
styleswitch.js on your page, or any conclusive search results what it might entail.
Show us some code or a link to it at least. ;-)
What I would advice is to have a look at the page source with Firefox. Stray tags are displayed in red which is always very helpful. There are quite a few in there.
Cookies in the form of
localStorage are indeed quite simple to create and have great backwards compatibility but require some JS.