You know - there is a fulltext search tab possible for any CHM.
HH Workshop API documents how to move to the search tab and initiate a search. Unfortunately the initiating a search part has always been broken in HH. The only way around this would be to find the HH window and search pane controls. Then control those controls from your application using via low level Windows API calls.
I translated this for working with Visual Basic 6 a long time ago. So the search string is pushed to the CHM search tab and search is starting. http://www.help-info.de/en/Help_Info_HTMLHelp/hh_api.htm#Search
Disclaimer: This isn't a product link - only code to help (open source).