I've wondered the same thing Magnum, and here's where I think I come down...
If you're in captivity among these animals, there isn't a thread of a chance you're going to prolong your life by renouncing the Christ Jesus. Not a chance. You're just as dead whether you renounce him or not.
Can you imagine, being brought by terror to the point of renouncing Christ - and then the shame of begging his forgivness in your final moments before execution? I can. And it feels a whole lot worse than knowing in that final moment that I did not renouce Him.
So while I think every fiber in ones being would scream to do everything possible to save ones life, I think that at that very moment - the moment I had to decide whether to renounce Christ or not - would come and go without such a renunciation.
All that said, I'd rather focus on killing them before they kill me, thank you very much!