Can't speak from experience about the Encore (only one I have wears a buttstock), but have handgun hunted with Contenders, BFR and X-frame S&Ws. I am not an expert, but here's some thoughts from my experience:
In the field, your shooting is going to be no better than your rest. If you're inside of a distance you can keep 'em in there offhand or whatever, fine. Otherwise, get the gun supported.
A daypack or similar, your gloves or shooting mittens, hat, whatever, can be laid on things to pad or bulk them up for a better rest or to build a rest on the ground itself to shoot behind in prone.
There's a mess of different shooting sticks on the market these days, many of which are collapsible/adjustable for length and can go from sitting to standing height. There's also the homemade option, although quick and easy adjustability is usually not found there so much. Sticks that can double as a walking staff are nice and are in hand if the opportunity comes up to use them, sticks that collapse small enough to fit into/lash onto a daypack or other gear get out of the way when you don't want/need them.
If you're hunting from a ground blind, elevated blind or tree stand, some thought and effort beforehand goes a long way into making sure you've got support where it's useful.
I like the big round haybales; a little padding and you can have both front and undergrip support like with dual bags off a benchrest. Plus, if you're tight with the farmer/landowner, you can get some positioned where you want and essentially end up with a round bale blind.
Handrifles are often clumsy. For me, easiest is keeping it in the crook of an elbow, pointed outboard or suitcase carry around the midpoint. A sling or holster (for those they're made for) is nice for when dragging a deer, scrambling around in and out of steep ditches, climbing into stands, etc. But be warned. Sure as anything, it's when the gun's out of one's hands that the darned critters show up at chip shot distance and stand there staring.
One last thing; practice with whatever kind of support you're looking at using. A front and rear rested gun can shoot to a different point than just a front rest. Shooting sticks aren't completely steady and often have quirks about where they head off to when the pistol recoils; better to know what to expect in advance.
