Avoiding 301 redirects

You could handle it from the htaccess file. How big of a site are you talking about?

Alternatively, you can use redirect_canonical filter as described in this post: https://www.billerickson.net/code/how-to-handle-redirects-in-wordpress-via-otto/

I know I can handle it with the htaccess file, however this would mean using 301 redirects – I do not want to use 301 redirects, I want to keep the url structure the same as it currently is.

If you use relative url references in mod_rewrite, the redirect returns 200. This is how permalinks work.

How does one go about using relative url references?! Any links you can point me at?

Only need to use this on Pages I think

Short answer: don’t.
WordPress’ handling of relative urls is unpredictable at best.