You shouldn't try to flee FROM combat, you should withdraw BEFORE combat, which makes it harder to determine what's the correct action. That's not always possible, of course, but you frequently have the option not to confront dangerous opponents.
The only combat you can flee from is basically the one in which you have the upper hand, but an exhausted enemy with a bow and a (virtual) quiver full of arrows is still dangerous, so if you're not equipped with a bow (and arrows) and have taken more than light damage you should at least consider whether to withdraw.
Edit:
Fortunately, hired NPCs seem to be as resilient as Njerps and robbers. I just suffered from vermin problem in my farm plots (a Njerp warrior equipped with bow and shield, plus scimitar), so I hired an adventurer to help removing it, as my character isn't a great warrior and is injured as well. The end result was an adventurer with 10 wounds, one of which was serious, without passing out, a dog with at least 3 bad wounds, and a PC with two additional wounds, plus a dead Njerp, at the end. I should have hired 2 adventurers, and would have, if they didn't keep refusing, and 2½ to 1 seemed like good odds.
Injury doesn't seem to affect fatigue buildup when swimming, and I haven't seen it for other tasks either (but swimming is particularly easy to spot at low skill levels). Injury definitely lowers movement speed and gives success penalties to heavier tasks (very easy and possibly easy seem to be unaffected by encumbrance and injury, as long as an essential body function isn't disabled).