i virtually never let anyone touch my housing. After a dive, I lift it onto the swim platform, giving the crew the obligatory "no thank you, I'll take care of it". Get out, grab camera, dunk, find the safest spot on boat for it. On a dive trip, I make it very clear the first day I'm the only one that handles my housing, unless absolutely necessary, like chuckin seas or a raised deck. Even then I hand them the camera such that the handle's the clear thing to grab, and only have them to hold it while I get out. I've seen too many screw-ups and spent too much money to risk otherwise.
It amazes me when I see people hand off their cameras from the water and just go get cozy on the boat. Then I look into the rinse bucket to see multiple cameras/computers/torches piled thick, sloshing and banging into each other on a bumpy ride back. No, thank you.
Imagine this on the 2nd day of a liveaboard:
my friend and another guy have very similar ikelite rigs. The crew grabs my friends unlatched rig off the camera table and hands it to the other guy in the water, then swapping it out when the guy sees its not his. My friend returns to find his rig in the same spot, but completely flooded (they haddn't even noticed). Yes, this happened, though luckily the operater was willing to replace it.
I never bother with a carrying strap, i find the handle works fine and the rig's already got too many bits & pieces - a strap would just get in the way. Though the above posted short rope with clips would be the least obtrusive.
Strap or not, if you repeadly place your trust in random people to handle something that expensive, delicate & specialized you're just setting yourself up for catastrophe imho.
Cheers,
Chris