Hi,

Is there any way to change the default search plugin used by K2 search box from Joomla search to smart search?

No, I'm afraid not. You need to use the smart search module in order to achieve this.

I was thinking maybe tweaking the code in this file: /plugins/search/k2/k2.php

by changing this line of code:
require_once (JPATH_SITE.DS.'administrator'.DS.'components'.DS.'com_search'.DS.'helpers'.DS.'search.php');

to include com_finder and finder.php

something like this:

require_once (JPATH_SITE.DS.'administrator'.DS.'components'.DS.'com_finder'.DS.'helpers'.DS.'finder.php');

I've changed this line and nothing happened. I am thinking of renaming and replacing all search files with smart search ones.

What do you think?

I'm not quite sure that this will work. Why don't you try the smart search module instead?
Maybe this proves helpful as well docs.joomla.org/Smart_Search_quickstart_guide