This works either way

If you just wanted to search the site rather than search the web, you could remove the ability to search the web. (the radio button).
Edit:
Find:
PHP Code:
<form action="http://www.google.com/custom" type="hidden" method=GET name="search"><td class="thead">Search Site / Google</td>
Replace with:
PHP Code:
<form action="http://www.google.com/custom" type="hidden" method=GET name="search"><td class="thead">Search Site</td>
Then
Find and Remove:
PHP Code:
<input name="sitesearch" type="radio" value=""><a href="http://www.google.com/search"><img src="http://www.google.com/logos/Logo_25wht.gif" border="0" alt="Google" align="middle"></A>
This should work, although I've not tested it.