Ethically as a hunter, you should ensure that the animal you shot at die right away with your very first shot,
even if their body does not realise that it is dead (and runs for a few seconds).
By taking a shot at a running animal (or over a very long distances),
you are giving into chance that it is wounded.
I am not going to tell you what to do ,
but my respect goes to hunters that let an animal go if the shot is chancy.
As Pumpkins said, there is no reason to "have" to shoot it.
It has done its part by being alert enough to detect the hunter,
OTOH, the hunter has not done his part by stalking correctly.
I live in civilised (hum) society, so my live is not at risk daily..
But if there is a society breakdown and someone trying to kill me,
I would rather to be shot and dead by surprise.
Not shot while running in fear, nor die of a festering wound.
Thus brought me into "The Wish"..
I wish to be shot dead..
at the back of my head
by both barrel of a double barrel shotgun
by a jealous husband
at the age of 99