I'm going to go out on a limb and give a sort of non-TGO answer because it seems like you already know the answer and this is more psychological.
So, my attempt is humor.
If we look at the data (unfortunately death statistics in the US is now considered private, so I'm using pretty old data, which can be found here. https://www.wemjournal.org/article/S1080-6032(97)70944-X/pdf
Also, my methodology here is going to be terrible, because I'm focusing on humor over actual context (but all claims are technically valid).
First and foremost, buy a lottery ticket right before you go hiking and carry it with you. Your odds of dying to an animal attack are roughly 0.65 in 1 million. Your odds of winning the Powerball jackpot are roughly 0.33 in 1 million. If you combine the two the odds are so low that this is literally never happened so you're probably perfectly safe. Alanis Morissette posits that it's at least possible to win the lottery and then die the next day, so if you're really worried about it and decide to use this technique you might want to limit your hiking trips to single day excursions.
Second, you might want to see a doctor and find out if you have an allergy to bee stings. About 28% of the already exceptionally rare deaths from animal attacks are bees/wasps, making them the most deadly killer of humans we know. They have a great PR firm though after that whole honey incident back in 2007 (https://www.imdb.com/title/tt0389790/) so people don't really know and aren't crippled by fear of these deadly predators. Bees man, they're EVERYWHERE!
Another 24% of animal related attacks from above are marine animals, and while I don't have a breakdown of the statistics for that, unless you're killed like this man (http://www.xinhuanet.com/english/2019-07/04/c_138199406.htm) who swallowed a live tilapia and choked on it, I think we can safely exclude this category from your hiking-related statistics.
Of course, I'd be remiss if I didn't mention to take the ACTUAL advice on dealing with bears, cougars, and snakes, in particular (but don't forget centipedes and scorpions if you want to be extra cautious) because that's really your best bet if you DO happen across wildlife. I recommend this option over my next one because it's also better for the wildlife, which, if I'm being perfectly honest, I care about as much as I do you (no offense).
Lastly, if you don't want to learn anything about how to be safe while hiking, keep a journal. Now, I only have one data point to extrapolate from, but if you go blindly wandering around into the wild with no preparation, knowledge, or experience but you keep a journal and die, a movie is made about it and at least your legacy will be overly romanticized and win tons of awards.