A lot depends on the air tempture and where the shot hit.
I do a few pictures and then field dress then you can pose the deer to get more pictures after that. You should have no problem getting a few pictures and dressing a deer in an hour.
Where I hunt you don't normally have a problem hanging a dressed deer in the shade for a couple days.
Washing a deer's cavity out in a stream I feel is just asking for trouble. I can't think of any place in the lower 48 with a streams water clean enough you can use it as potable water.
Al