Search.php currently has a php "else" conditional statement that prints your "no posts found" message. You ought to be able to replace that "no posts found" message with some more php code that does a redirect.
Here's
a link that says you can echo a meta-redirect using php. I have not tried it.
--- code for inside the existing "else" loop --
echo "<META HTTP-EQUIV=\"Refresh\"
CONTENT=\"5; URL=html-redirect2.html\">";
--- end of code --