I always use a rest and I support the gun over the forward part of the frame and the Pachmayr fore end (TC Contender). Longest shot I've made on any of the five deer I've taken with it so far is about 90 yards, but I shoot it the same way at the range off sandbags. I WILL NOT take an unsupported shot beyond about 30 yards, just will not. With a proper steady rest, my TC in .30-30 is effective right out to 200 yards. Finding a good rest is just part of the handgun game in the field. I've shot one animal off hand with a .357 magnum 4" with irons, about 40 yards on a Javelina, and I trailed that thing 300 yards though the brush before being charged and finishing him with a shot to the head. I hit him too far back, behind the shoulder. A rest could have reduced the likelihood of a bad shot, but I was stalkin' this group of stink pigs over open ground. They were down in a dry wash.
My stands on my place have gun rests and I've taken 3 down there with the Contender, the other two out of box blinds that had rests. When I've used my Blackhawk, I rest it up just in front of the trigger guard, more solid than laying my hand over the rest, less error. I've taken two with the blackhawk 50 yards and less. I have a pair of shooting stix, but I've only used 'em in east Texas hunting squirrels with the .22LR barrel. They work well, though, if you're sitting on the ground. I find a tree to lean against when I'm squirrel hunting and I can lay down on my back and get shots way up in the trees off those stix, or if I'm walking I can rest on a tree. I can also lay on my back and clasp the gun between my knees for support when shooting up in the trees, done that successfully before I got the shooting stix.
JMHO. I've only got 7 deer and a bunch of squirrels with handguns, but that's how I've done it. Go to the range, shoot groups off sand bags, then try different field positions. I do this all the time with my Contender and Blackhawk, sit and shoot off the stix, brace using the pole that holds the cover over the shooting benches, etc. Handguns are like bows, if you don't practice the skill fades a bit. Creedmore is a good position, but not practical in many hunting situations. I shot IHMSA that way, works, but just ain't too many places you can lay out in a grassy field and get a shot.