If you know php and html, you could try to modify a few lines of code. BIG CAVEAT: my server is down right now, have not tested! (Of course, back up files first ...).
The search code appears to be isolated to mod.search.php in the search module file. If you open mod.search.php, search for the phrase “search_any_weblog” and you’ll see the code.
If you want to eliminate “any weblogs” for all you EE sites, you can modify the module code and comment out the line that outputs that html line, and initalize the string ($weblog_names) to “”. You may also want to set another option as default, and check that there is at least one weblog when building the list.
If you don’t want to eliminate the “any weblogs” you could put at the bottom of the select list (and select another option as default).
You can also change the wording of “any weblogs” in the language array (or whatever it’s called). Check out lang.search.php in the language directory for the variable “search_any_weblog”.
I seem to be limited on how much “code” I can post, so these are just rough directions.
M.