CDN module enabling "Far Future expiration" breaks whole site theme drupal 7
These modules might help you out (quotes added here are from their project pages):


Advanced CSS/JS Aggregation:


  
  On demand generation of CSS/JS Aggregates. If the file doesn't exist it will be generated on demand.
  Stampede protection for CSS and JS aggregation. Uses locking so multiple requests for the same thing will result in only one thread doing the work.
  Fully cached CSS/JS assets allow for zero file I/O if the Aggregated file already exists. Results in better page generation performance.
  Can add JS to any region of the theme &amp; have it work and be aggregated.
  Combine CSS files by using media queries.
  Prevent more than 4095 CSS selectors in an aggregated CSS file (IE 6-9 limitation).
  ...
  

Imageinfo Cache:


  ... will generate image styles right after an image is uploaded and also on entity save. This will help with front end performance as the needed image style will already have been generated; thus the end user doesn't have to wait for the image to be generated. This can also mitigate some issues with image style generation if your CDN is configured incorrectly as the images will be generated without the request going through the CDN.