Maine is an open carry state. I do not believe they can tag you for hiking in the Maine woods with a open holstered hand gun. If you were openly carrying a shotgun or rifle in the woods they might have a case. Concealed carry with out a CCW while actively hunting is also legal. But only while actively in the woods hunting with a hunting license.
Other wise concealed carry without a CCW is illegal.
I also believe a gun in a case unloaded in a back pack would be legal as well. The law reads that you cannot without a ccw have a concealed gun on or about your person. In a case, in a backpack would not meet that standard. Just in an outside pocket on your back back I think would.
IMHO, I think for your purposes and with out having a CCW, I would carry a loaded open carry holstered handgun. Just keep in mind, that while it is legal to open carry up here, I have never scene it. If you are deep in the woods I cannot imagine anyone else getting upset about seeing someone with a gun and attracting attention to yourself. However, if you are hiking on a very popular trail with lots of out of staters or Portlanders, who might attack some attention, although you would still be legal.
My opinion is worth what you paid for it. Maine has a very good searchable law website. I suggest you tackle that to make sure. Have fun.
BTW... Mountain Lions in Maine? It has not been confirmed yet.
The best bet, for your next trip, is to get a Maine CCW.