I'm not sure what you meant by the "local". Do you mean
opening the Index.htm directly (from filesystem) in the browser? It would be tricky because there would be no web server running the searching code there and what you have at hand would be only browsing scripting.
What is the scenario you want to make the documentation browsable in? Maybe you could use a convenient solution like I did. Let me explain it.
The only SHFB output target where searching is not available is the website output in the pure HTML (Index.htm). All the others support it (ASPX, CHM, HxS). What scenarios is the Index.htm meant for? To open the documentation locally from the filesystem
or publish on a web server without ASP.NET. Luckily, I covered the first scenario by the CHM and the second one by enhancing the output of the SHFB a little. If you want to put your documentation on web without an ASP.NET server, that would be it.
Search was trickier because loading the full-text index to the browser and search through it would be too slow - even if it would be done only initially and then read from the cache. I actually ended up having the magnifying glass icon next to exercise book