It's possible to use mod_pagespeed to minify HTML without using a cache. Use
ModPagespeedRewriteLevel passthrough
ModPagespeedEnableFilters=remove_comments,collapse_whitespace,elide_attributes
ModPagespeedLowercaseHtmlNames on
This will not touch the CSS, JS, or Images, but will aggressively minify HTML.
mod_pagespeed requires its cache to make any optimizations to CSS or JS files including minification. In theory we could rewrite CSS and JS files on-the-fly without a cache but that would add latency & compute overhead to the server under high QPS -- that's why we designed our system to use a cache. Although now that I think about it, we do minify *inlined* css and javascript without a cache. To enable that functionality without caching you can add
ModPagespeedEnableFilters rewrite_css,rewrite_javascript
ModPagespeedDisallow *.css
ModPagespeedDisallow *.js
This will, of course, not minify external css and js files.
Can you explain why you don't want a cache?
-Josh