Ah, that makes sense. You can definitely make stuff private on itch: at the very bottom of the "new project" page, choose "Restricted" instead of "Draft" or "Public". You can choose to set a single password that you can give out, or (more flexibly) you can go back to the game's Edit page, choose the "Distribute" tab and generate one or more download keys which can be claimed by an individual person or revoked so you have more control.
I suspect they won't let people add restricted games to the jam, but as jam owner you should be able to come back and add it once they make it public: I'm nearly certain that you can make whatever exceptions you want to the rules about when people can submit games.