Inch,
I am aware of your past scare - but even if I weren’t I would still recommend you not over-think this process.
To begin, a person can hang wrapless with virtually any hanger, and in my personal experience the Bib is very good for this. I want to stress though, that I am not a heavy weight hanger myself, so I can’t speak to how well a wrapless hang would go with the Bib at over appx. 10 lbs.
That said, the purpose behind wrapping has more to do with comfort than anything else. Other considerations such as bunching skin and tissue, providing extra dorsal nerve protection, controlling glans bloating/pressure, and preventing slippage all come into play, but to a lesser degree than simple comfort - especially if you are using a well designed device.
The way I have used Bib’s Starter without wrap is to pull a flaccid stretch holding from my glans. With the device in the palm of the other hand I lay my stretched shaft into the well of the device and gently close it (think closing a book in one hand). If done with care the top bolt will land in its proper position and I can begin tightening.
At first, you should not concern yourself with how much skin ends up where. Simply pay attention to your settings and allow that you will have to tinker with them until you find a good place. Once this is done, you can then give your attention to skin issues - which should be easier now that you are not at war with your wrap.
One issue that often gets over-looked but is almost always the source of a hangers problems is wrapping; how much material, what kind of material, how loose, how tight, what direction, what kind of placement, etc. Sadly, a bad wrapping technique can turn a good device into a worthless peice of junk.
This is why I stress that you attempt hanging with your Bib sans wrap. It is a well designed device and if used properly will never be the source of any physical injury or discomfort. I use the Wench, which is less friendly to a wrapless hang, but even then I use only the smallest amount of Theraband and keep it very loose. It’s sole purpose in my case is skin comfort.
Your problem(s) with going cold in more areas of your anatomy than your unit is, frankly, unlike anything I have ever heard of.