Ohta-san the master of the ukulele opens his side in order to support the neck. Pinch grip in your first option is wrong (see the right figure). I think your second option is similar to his right example (left figure).
Thanks for the photo. After following this thread, I’ve decided to try to practice playing Ohta-san’s way, opening up my fretting hand side, and after a few days of making a conscious effort, here are my observations:
-My grip with the fretting hand, keeping the thumb behind the neck, is much more comfortable to maintain. I think my poor technique previously has been due to comfort of my hand when playing with the elbow closer to my body.
-Both proper arm position and grip have made holding the ukulele with the top facing directly away from me infinitely easier and more comfortable. With the “wrong” posture, I frequently was frustrated by how difficult it was to keep the top from pivoting up towards me while playing. With the “right” posture, I have to strain to make that happen; the top wants to face out towards the audience, period.
-What were once difficult chords for me to fret are becoming easier to hit cleanly, largely due to the different attack angle my fingers have when using the right posture. This means my fingers don’t feel crowded on chords like Dm7 as they once did, AND are less likely to be accidentally muting an adjacent string.
So again, thanks for sharing. The one thing I’ll add is that practicing correctly now, after years of doing what was comfortable and wrong, is a serious effort. Thankfully I know from experience that practicing with intention and with repetition can overcome even the most ingrained muscle memory.