This is kinda what I thought. It makes my irrational fear a bit more irrational I guess...
I would be reluctant to call your fears irrational. Maybe fear due to lack of education on the 2 subjects (sharks & cave diving). They are real fears to you. Fear is not always a bad thing, it is a tool to help us to survive. When it becomes irrational is when the individual refuses to educate themselves on the topic(s) that is causing the fear & using that fear as an excuse to not educate themselves. After education, then if there is still fear, then it is a founded fear. Read up on the hunting instincts & tactics of sharks & various species common to the areas you will be diving. Also read on the skills & rules taught to cave divers, the what's, why's, how's, where's, when's & who's of cave diving, though these will never take the place of good, proper training to do this kind of diving. There are many resources on these topics, including here.