Shark Handling

I've caught Dogfish, Leopard Sharks and Soupfins (Topes) and hooked a Thresher.  I've always been wary of their mouths but not sure how wary I need to be. They can all cut line, but I've been told that you can put your hand inside a leopard shark mouth with no consequences. I don't trust that, but how careful do I need to be with those versus Soupfins, which do seem to have small sharp teeth versus Threshers, etc..  Seven Gills definitely look like they could take a finger off and are twisty and squirmy to boot.
On Threshers it seems the tail is quite a hazard but I assume they could give a bad bite as well.
When I caught that 5 1/2' Soupfin a few years ago I was afraid to hold it (after seeing that video of that dad losing a finger to a small Black Tip) and had Pat hold it for a photo.
I did get bit by a 20" halibut once and that wasn't fun but it wasn't going to take my thumb off.

Any experienced rundown on these various species and what damage they can do?

I’ve been fortunate to only catch sharks from the shore or a boat.
With a kayak, I’d likely cut the line as close to the hook as possible and let them on their way.
Here’s a photo from 2010. One hand around the caudal-peduncle, one hand just below the pectoral fins.
Worked for me for leopards **from shore**.

Sevengills have a mouth full of razor blades, keep your hands away, get the hook out with pliers.

I had a 3-foot Mako up to the side of the kayak once.  I didn't really know how to ID the good-eating Mako at the time, so decided on CnR.  I did think about trying to recover my lure, but, fortunately, he broke off before I could do anything stupid.  All sorts of crazy teeth pointing in different directions on that fish.