I had that concern when I first started journalling, and invented a secret script (neography). I stuck to it a week or two before I realised nobody really even cares about most of the stuff I write about, so why make the effort. Mind you, I'm young and don't live with a partner, so I don't have to worry about them finding my journal.
A partner who is an ethical person typically would respect boundaries, and avoid snooping (e.g. reading journals and going through unattended laptops/phones). However, as a failsafe (e.g. the person has a lapse in judgement, they're drunk, or is typically great to be with but struggles with snooping), just don't commit anything offensive or relationship-ending to long-term storage.
For example, if you're having doubts about a relationship or feel concern about a sensitive subject to the other person, you can write your thoughts to work it out on a separate piece of paper to securely dispose of after, or (similar to a suggestion elsewhere in the comments) a text file that isn't saved or gets deleted after.
Some may argue for great openness about thoughts in a relationship, but I think it's often useful to work things out on your own to clarify your thoughts and position, before a crucial discussion.
I like writing on paper much more than typing after years of being mostly paperless, though experiences may vary depending on personal preferences.
The main benefits include the flexibility to easily draw and write formulae if thinking about a technical topic, the ability to recall what you write easier than what you type, and enjoyment of the feeling of writing on paper. The feeling is actually really nice, and I believe it even inspired essays by Japanese authors about the feeling. The Guardian interviewed some researchers about the differences at: https://theguardian.com/science/2014/dec/16/cognitive-benefi...
The main drawback is the ability to search, though I personally rarely look back at past entries (the main benefit is during the act of writing). When brainstorming about something work-related, though, I do scan the related pages with my phone. Digital handwriting (e.g. Surface or iPad) with an app that does hand recognition is an alternative, though the feeling of writing with a good pen on quality paper is much nicer than a stylus on the display (even with screen protectors that simulate paper).
If you’d like to try, you can get an excellent setup for less than $50. You can get a nice pen (Pentel Energel, Zebra Sarasa, or Uniball Signo) and notebook (Rhodia, Midori, or Leuchtturm1917) and try it out for a few weeks. r/pens and r/notebooks talk about the differences, and also suggest other alternatives for writing tools.
In my journaling I realized the process of writing was valuable, but I rarely referred back to anything. So for personal / stream of consciousness things I either write on paper and put it in the shred pile, or to something like an ephemeral vim buffer.
For when I'm feeling very self conscious I have a script that turns off echoing to the terminal and streams everything I write to the clipboard (in case I decide I want to review/save after all)
To double down on obscuring the knowledge that the journal exists, if a person hasn't yet started a journal, a very good habit is just not to tell anyone you have one.
If anyone occasionally happens to see you writing in a journal and asks about it (though preferably it's best to save writing for private moments), you can just describe it as note-taking or brainstorming. If one considers these lies by omission, a more direct way would be a description of "personal notes." Then, the notes sound far less interesting for most people to look into.
I've written my own program that loads and saves my files with encrypted zip files. C# and .Net make this a breeze to implement. I use a long password so even if someone gets the file it will be hard to crack. I don't encrypt that many files, but sometimes I need the option.
