I bought a locking journal cover (like this one -- not the exact one, but similar) When you've filled the journal you can just replace it with another book of the same size. For the finished journals, either get rid, or keep them in a box somewhere safe?
Also, Microsoft Word, LibreOffice, and OpenOffice all allow you to save word docs with a password. You can even save the file name as something inconspicuous like "history_notes.doc". If you don't tell anyone you're using the PC to journal, no one would even know to look for it. (Just don't forget the password!)
(I have the same trust issue with journaling so I think about this a lot!)