A Ball Catch might meet your needs. I have a couple of sets in my home. In my case the doors do not have operable handles, just fixed. These are installed on the top of the door. In combination with the ball catch, you could tape over the opening in the striker plate, but that probably wouldn't last long.
Also, how often would you "want the door to latch?" ...A few times a day, once a week? Once a month? Tape would be an awkward solution if you wanted it to latch frequently.
A ball catch would keep the door closed, but still allow for just pushing the door or pulling the handle/knob to open it. If that works for you, you might consider simply removing the latch from the door knob completely. It would require taking apart the door knob, but that's a pretty simple matter. It would also allow you to revert back to a functional door knob/latch later if you changed your mind, sold the home, etc.