Plainly stated, it should not be the defining factor when purchasing a handgun for this purpose. User fit and ease of handling should, and that depends soley on the individual.
I've hunted with DA's, SAs, contenders, never worried about "fit". If they didn't "fit", I went grip shopping. I have a Pachmayr Presentation on the TC, an odd zebra wood finger grove grip on one of my blackhawks (feels real good for shooting, though it doesn't look traditional), a set of Ajax stags on my .45 Blackhawk, and usually Hogue monogrips in rubber on my DA guns or a Pachmayr Gripper. They are all different, but I shoot 'em all well enough. I adapt to the platform. Be a dull life if all I owned were Smith N frames. I really like SA guns for the way they handle recoil. A hot .454 Casull out of a SA gun is easier for me to shoot than a .44 mag out of an N frame. The gun just rolls in the hand on recoil.
That gun fit thing, I could never figure out why people were so set on "fit". It ain't like a shotgun. You can change your grip. I can shoot glocks, 1911s, revolvers of all types, even P08 Lugers. Ain't dropped one in the mud, yet, because I couldn't grip it properly. A gun should point naturally for self defense, but for hunting, you're not point shooting, you're AIMING and usually through a SCOPE! Being used to the grip of a self defense handgun is important for quick draw and sight acquisition, but on a hunting handgun, I care more about how the grip handles the recoil of powerful loads than how it "fits" my hand.
Contender grips can be awful in this regard, but my .30-30 12" hunter barrel is compensated. While it's loud, it kicks about like a .38 +P in a K frame.