Can spontaneously killing no-name hunters hurt my game?

Solution 1:

Skyrim lets you kill most people. The worst that can happen as a result of your (mis)deeds is preventing yourself from starting / finishing a particular quest or misc. objective.

If the character does not have an actual name, i.e., Hunter, Bandit, or Markarth Guard, they are totally killable (and in fact, tend to respawn after a few days) with no real consequences (other than potential bounty / murder related issues involved with killing them in the first place).

See here for more info about killing important people.

Solution 2:

So long as you are careful to avoid the bounty I'd guess you should be OK. Also: there may be others settings bounty hunters on you, be wary of those if you are low level.