Earlier quoted context omitted.
If you can live without the bang, you could just add a search engine to Chrome with the text "gh". Then, prepending "gh" to a search would just search Github.
The thing about bangs is that it's a curated, auto-updating list of shortcuts though. I could install my own but with ddg, I just throw a ! in front of the site and usually it works!
!gh { https://github.com/search&q=$QUERY$ }
!ebay { http://www.ebay.co.uk/sch/i.html?&_nkw=$QUERY$ }
Then all browsers (and other apps) could provide these standard shortcuts in their search functions.