Hey,
Depends on the sizes of your HTML files and on how many you have. You could embed those HTML files if you wish but as you mentioned that you wish to use a search function, parsing the content into a SQLite DB would be better and faster. But that also depends on the file sizes and on the amount of files. Keep in mind that some people rather not download huge apps. Think this through to keep the performance high.
I prefer to use databases instead of local files to search through and to display. There are many blogs and posts on the internet, out there that go into details about this subject.