I think the most Cobra outcome of Ozzy dying will be Cobra miraculously not being phased about it at all and moving on with no problem, like he did with Puff. He was crying tears of sorrow about the fact that people have cancer and aids in his phone-breaking meltdown stream but I have never seen him show a shred of genuine emotion whenever someone in his chat inconveniences him by bringing up the dead lizard. Its always a gruff, terse "I hope I find him in Spring" and then quickly left behind.
I'm not saying he won't get drunk and a bit bummed out, he probably will have quite a reaction the day it happens because he will finally check after trolls tell him and find out its true. But, I honestly could see him taking Ozzy's death better than most expect.