Experience,
As I read your posted intentions, it sounds to me like you are considering coyotes and possibly turkeys as targets of opportunity. If so, I understand your inquiry much better. The shotgun is fine for such a task. large shot in the #4 so should do the job at reasonable ranges. Afterall, you are not actively hunting these prey. If you were, the 22 LR would be my choice for the coyotes and the bow, my choice for turkey. Walking thru the woods, carefree is likely to yield no more than some poison ivy rash than a predator or turkey. But you'll be armed for it nonetheless.