A 404 by itself is not necessarily a bad thing. For resources no longer available, it is the correct server response. The only scenario where a 404 is bad is if the resource needs to be found, either for indexing or rendering.
As Simon pointed out above, search engines will fetch and index a resource anew if they see a new URL. Thus, it will not impact rendering or what's been indexed.
I used to manage a Drupal website where the lead developer set up CSS files to have a random number at the end of the URL, and those numbers got dynamically regenerated every couple of weeks, to keep search engines from caching the CSS for too long, as changes were frequent. It caused issues in Pardot landing pages (a marketing automation system), but SEO was unaffected.
Related: I use the noarchive meta tag on all website content, globally. This prevents search engines from storing archived snapshots of websites. Rankings remain unaffected.