There is a very interesting documentary on this expedition. One of the guys mentioned that when the grabber arm broke, they could see on their monitors an ICBM slipping through one of the tubes, heading down the bottom. Everyone in the room braced for the impact with the ocean floor...
1. it's practical impossibility to make unarmed nuclear warhead to explode spontaneously. The worst thing that can happen is conventional explosion that spreads the contents into the sea.
2. it's ancient fission bomb designs where water getting inside the warhead slows down neutrons and starts the chain reaction.
I'm 99.9 percent sure than no ICBM ever had the #2 types. Only bombers had them few decades. Even if there were, putting one into a sub would be the definition of insanity. One mistake and Murmansk is gone seems too risky even for Soviets.