Wow. Does sound like the back of the barrel is out of square. I think if you open the cylinder and lay a straight edge against the back end of the barrel and horizontal, you'll be able to see its edge not perfectly perpendicular to the barrel.
All you need to is cock the gun and let the hammer down. The bolt latch should stay in place until either it is cocked again or the trigger is pressed double-action style.
Looking down a gun barrel is not normally recommended, though I don't feel too badly about it if I open and check the cylinder and don't let the gun out of my hand until I'm done looking. If I do, I'll open and check the cylinder again. That said, the safest practice is to point it into a mirror and look at it that way. The mirror has the advantage that you can often bounce a flashlight off of it that illuminates the bore at the same time for a better view.
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