There have been a number of confirmed Mountain lion sightings in Maine in the past 30 years, confirmed via hair samples and tracks. What is debatable is whether or not the lions are part of a
residual population, or just passing through, as the last Mountain lion was killed in Maine around 1936. Timber wolves, on occassion, have also wandered over from Quebec and have been shot here in Maine (DNA verified). Federal offense to shoot either, unless it was a
verifiable self defense situation. Better be legitimate,
or it's SERIOUS trouble. Neither are supposed to be in Maine, but plenty of people still report seeing them.
That being said, Maine (as well as NH and Vermont), are relatively safe states. Even a reliable .22 sidearm should serve one well as a hiking / woods loafing gun. I have carried .22's, .38's, .380's on up to .44 Magnums during the course of my life living, hiking / hunting in Maine. Currently I'm packing an Uberti El Patron .45 Colt (or "Long Colt" if you prefer) for off duty carry, hiking, back up hunting sidearm, etc.). Feels REAL good in my hand and more accurate than I am. I was just shooting it this morning at a Florida State run outdoor range... Wicked smooth trigger. This Italian .45 Colt has been in my waistband / IWB holster the entire vacation. ZERO 2nd thoughts pertaining to my choice either.
Most would scoff at my choice, but I'm more accurate and comfortable with a single action revolver and that's what counts when the chips are down, not looking tacticool.
I say shoot what feels good and carry what YOU can make good hits with. Don't worry about what other people think or shoot. Pick a gun / caliber combination YOU enjoy and can shoot well, along with a solid holster to carry it in. Either a .45 ACP or 10MM should be fine for anything you may encounter deep in the New England woods.