For a long time now I have been advocating that the combat shotgun is the best form of secondary weapon for a Sniper and much of what is said above explains why. If you move around at night on your own...(we now work in pairs like your Marine Snipers but it was'nt always so)...ideally with the wind in your face to carry scent and noise away...you should hardly be suprised at what you bump into....but there is little or no thought given to this type of scenario when it comes to training.
FMJ .223 rounds are not going to do much on a charging bear...neither will they assist in a quick instinctive turning shot if a cat is up a tree...where as a shotgun loaded with a mixture of slug, buckshot and heavy bird shot would give you a much better fighting chance. Very effective on two legged suprises as well.
I have certainly had a few close encounters which scared me half to death but in fairness nothing along the lines of a Bear although in Africa we certainly were close to some Lions and Hyenas who thankfully were more engrossed in each other than us.
Spiders...Snakes...a Badger of all things...an angry heard of Cows...I have even had an Owl nearly take a chunk out of my ear...and a Hippo launching itself out of the water and up the bank when in Africa...have all taken their toll on my nerves......
Risks like this though never get a mention....as to sorting these problems out with a knife...well...good luck is all I can say and go for cutting the spinal cord as high up near the head as possible. Cutting throats would only work well if the animal bled out into the lungs so it choked quickly...but IF you can sever the spinal column it will go limp straight off.
This is not an easy thing to do however on predators whose skeleton and muscle structure has them armoured like tanks. If pushed I would pick what I am presently liking the most of the knives I have ...a Basic 9...it is long enough to get deep and not too deep in the blade so it can pierce well...plus it will be with me for it's other uses. Maybe a SHBM Jungle Assault with it's serrations might be a better choice...but you would need to be very lucky whichever way and in all liklihood the knife with you will not be selected for these reasons. Much as I think a Ruck might be a good contender...I doubt I would be carrying one.