Personally, I prefer a cross draw rig for hunting. I find it stays out of the way better when carrying my rifle slung over either shoulder and is more accessible when carrying a large back pack. I note that you live in N.Y. I live in Alaska. Here brown, grizzly, and black bears are commonly, unexpectedly encountered, sometimes with less than desireable results. Every year, there are several reports of maulings. Fortunately, none of my bear encounters have resulted in such. Regardless, I never leave home, not even walking the dog, or fishing without a minimum .44 mag, normally a 454 Casull, with hard cast heavy loads.
When deciding, you should do a few tests regarding accessibility. Try to draw an UNLOADED revolver from a strong side holster using your weak hand. Now try drawing a revolver from cross draw position using your weak hand. Much easier. Next, lay down on your back and try drawing a strong side revolver with either hand... kinda hard to do. Then, on your back try drawing from cross draw with either hand... you can do it. Repeat the exercise when laying on your left and right sides, both strong side draw and cross draw. You can try this "Mexicen Carry" with the revolver in your belt if you don't have the holsters. It will give you an idea of the mechanics involved. IMO cross draw is the only way to go for hunting, hiking, etc. activities, though not necessarily the best for CCW.
Now a word about holsters, the Bianchi 111 Cyclone is my holster of choice. There is enough wiggle room in the belt loops to help ease drawing with the weak hand from the cross draw position. You can actually grab the butt, rotate the gun in the holster and complete the draw weakhanded WITHOUT sweeping your torso with the muzzle. This is not the case with some other holsters that hold the gun tightly against the body and at an sharp angle relative o the belt. The DeSantis cross draw rigs don't work for me for weak hand draw. Someone mentioned the Galco Phoenix, I have no experience with these.
Just my thoughts for your consideration. Good luck with whatever you choose.