That seems to be the critical issue..... getting the choke on while not getting gouges by fingers (or knives). The issue is first "who is controlling who". If I have my structure, I may even turn the Hadaka Jime into a throw.
That's the main thing - do you have enough control to apply a choke? Do you have time? Do you have freedom (only one opponent) to apply a choke? Are you sure?
I've recounted this previously - a Canadian national team (retired) judoka got into an argument with another person at a bar in western Canada (pre 1990). Argument went to the street, judoka threw opponent to the ground and was applying some form of juji-jime to him (possibly nami, gyaku, or whatever - doesn't really matter, does it?) when opponent's friend pushed a knife through and through the judoka's chest. This, of course, ended the fight. The judoka somehow survived as the knife missed heart, aorta, vena cava, pulmonary veins and arteries, and spinal cord, but there was (AIUI) an extended stay in hospital. Don't know if a lung was punctured or not. I won't name the judoka.
You mentioned "cutter bone" - that's the radius. I believe you're talking about the one where you grip palm-to-palm with the radius across the throat, and pull like heck as if you're trying to take the guy's head off with your radius?
The way I was taught to do "rear naked choke" or "Police sleeper" or whatever is as was shown in those videos, above, but the idea was to get it on quite tight for starters, have the bottom hand grabbing your own biceps (of the other arm, obviously), have the top hand palm down on the back of the other's head, pushing downwards/forwards into the hold, hug very hard, and clench both biceps and all the forearm muscles hard. Makes for a very tightly held neck, high pressure inside the choke, and not a lot of room for blood flow. I've only rendered a few unconscious, but it took nowhere near 5 seconds if I had it on "right".
Severely out of training at present.