Vocal student and singing contemporary Ruth Libbey discovered this wonderful image/concept for non-judgemental singing. She writes:
A quirky tactic for singing: Imagine the pop, hiss, and scratch of an old recording (for instance an antique recording of Caruso or John McCormack) while singing any song. In your imagination, hear the gentle scratching sounds of the turning record as the needle is dropped, before you even sing the first note. Imagine these sounds continuing while you begin to sing, and right through to the conclusion.
If you can do this, it becomes like listening to someone else from long ago, not to yourself now. This lets you drop right into your singing experience instead of standing outside judging one thing or another. It lets you forget obsessions with technique, worries about breath or posture, concerns about what you’re doing with hands or face. Instead of worrying about the next phrase you just enjoy the entrance of the melody as if listening to an old recording of someone else from a faraway time and place. You can relax; listening to “someone else” you don’t need any of your habitual singing tensions. It gets you out of the way so you hear and appreciate your own singing without overthinking or interfering.