Well, I tried it I just can’t seem to trust all my weight on my shoulders. As soon as I easy my way all the way around, I’m about to settle in and I let go. For reference, I’m 100kg and in my mind I think my weight is going to hurt my shoulders. Is skinning the cat safe for me?
Getting comfortable with spinning around upside down is usually the first hurdle. Much like teaching freestanding handstands to new trainees, it takes some time to get over the initial disorientation that can occur.
As for being safe on the shoulders, just like is suggested in the video you posted, it is always a good start to find a way to hold the position with the feet supported. You can either get into it like Twyman suggests, or you can set the rings at a height where you know your feet can touch the floor, do the full skin the cat and then touch down on your feet. Set the rings at a height that will allow you to simply let go of them instead of pulling back up through the movement.
The bottom of the skin the cat, where you are hanging in deep shoulder extension, is called a German Hang, in case you would like to search for more stuff.
When I taught at a gymnastic strength training gym, there were plenty of people 200-ish pounds, and some significantly bigger. It's possible; it just takes careful progression. With moves like these that have the potential to overload soft tissues
if loaded inappropriately , it is always best practice to start pretty gentle and see how it treats you. Then, over time, gradually expose yourself to higher loads.
All that said.... I think these are going to enter regular rotation for me. I've barely done them in a while, and doing just a few sets the other day had my whole shoulder girdle worked pretty good.