I found myself looking for the same solution today, as I am seeing more and more false positives due to this. I'm surprised that there seems to be no way to exclude attachments from searches.
I haven't taken the plunge yet, but I think my solution will be to strip out all of the attachments from emails so they no longer are present to be searched. This will require making sure any needed attachments are located elsewhere, but an email is really not the best place to store an attachment.
Of course, the ability to batch remove attachments also isn't present in Outlook, but there are some utilities online that can be downloaded to do it (some free, some not free). Some even have the ability to automatically save the removed attachments and include a link to it in the original email, which could be very helpful.
Actually, thinking about this, it still won't be an ideal solution, because someday you might want to search for things that DO have attachments. If stripped attachments could be replaced with a tiny placeholder file, that would be better because you could still use "has:attachment" search. But that might be asking a bit much. You win some, you lose some, I suppose. If there was a utility that removed only specified file types (e.g. .doc, .pdf, .xls, but not .png, .gif, etc), then that could be helpful too.