As duel says, all hospitals should supply the rubber topper things that open the bottles. My mentor has never shown/told me about them, but my second mentor did so it may be worth you asking.
I always hold the bottle by it's main body ensuring the dot is facing me. I then place my thumb above the dot with my finger behind, and break it away from me. It should break easily that way and as your fingers are on the bottle and above dot, they should be away from area that snaps.
Does any of that make any sense??? I hated snaping them at first and almost cut myself every time, but now I'm used to it and have the nack, I'm fine
I hope that helps, good luck