I want something strange: Google Custom Search, but without AJAX

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

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 :-(

I saw a couple of similar solutions for a narrower search, but completely without a clue how they are implemented.