I just realized, that this tip comes with a caveat. If you don't select a specific region, Search & Replace will still restrict itself to the UsedArea of the worksheet (or workbook, if you choose that option). This is a good thing. Otherwise, the operation would take forever, give or take a few minutes.
Still, if the UsedArea of your worksheet/workbook covers a very large area, this can still take a very long time, so you're going to want to restrict the Search & Replace only to the area that contains the null strings that you want to replace, if at all possible.