Stylesheet switching and caching

I’m implementing a site that allows users to switch stylesheets (to show a high contrast version for people with vision impairments). The switcher essentially just changes the <link>ref to whichever stylesheet is appropriate.

However, I just realised that this will lead to problems when I switch on caching (either using WP Supercache or W3 Total Cache) – as only one version of the page will be cached and thus displayed to the user.

Any thoughts on possible solutions?

I use W3TC, so these are approaches that I can come up with it for it:

1. Fragment caching to exclude that part of page, will reduce cache effectiveness overall.

2. Identify page with switched stylesheet by query argument, disable caching of such pages.

3. Identify page with switched stylesheet by URL endpoint, disable caching of such by mask.

4. Implement stylesheet switch via JavaScript (not really W3TC-specific).