Without a fridge I go by the old adage of the 40deg rule.
Which is simply that for fur game you hang it until it reaches a total of 40C which can be 10 days at 4C (10*4=40) or 5 days at 8C (5*8=40) or any combination there of!
With a fridge that circulates the air, this can be extended to suit more conventional hanging durations. With feathered game, I usually dress and either freeze or pass on to friends within 36-48hrs unless I’m gong to use it straight away.