I want strange: Google Custom Search, but without AJAX

I made a custom search engine demo Searching Tomsk sites , everything is good and even wonderful, BUT there is a problem: not all residents have access to the “external Internet” (outside Tomsk; the internal traffic is completely free).
Therefore, the question arose: is it possible to make search queries and answers pass entirely through a separate server that has access to the external network, and that city users only access this server without going to the external office?

Once there was a Google Search SOAP service, something there, but now it is closed and everyone is invited to use the Google Search AJAX API, which is completely unsuitable for solving my problem :-(

Saw a couple of similar solutions for a narrower search, but absolutely no idea how they are implemented.