Make a URL redirect and not "lose" the address in OpenWRT - is it possible?

Question

linux

Good day!
There is a router with OpenWrt on board and such a question arose.
Is it possible to redirect the URL from the client in a way that would not "lose" the address itself, and if so, in which direction to look and what problems can be encountered (the forthcoming problems with ajax are worried ...)?
For example, the client tries to get to google.com , and the router redirects the request to example.com/index.php?url= google.com
Many thanks in advance!
PS The problem arose due to the fact that all clients connected to the router, when going to any site, need to add a script to the HTML code of this site. I thought to do it through a web proxy, but the question arose as described above. Possibly "shove"script on the site can be in a simpler way? Thank you!