Lots of guys debone or quarter a deer and throw it in a cooler with ice. I don;t, but the guys that do recommend having one with a drain plug and leaving it open and on an angle to let the water drain out. I soak goose breast to get all the blood out all the time, so i can't imagine water is going to hurt the meat.
If you are limited on fridge space look at
meat lugs. They are wide and long and not tall. Many you can get 40 - 50# of meat in. I use them when curing goose breast as I can have a crap load in one and only take up one shelf. We also have a second fridge in the basement. It is just about needed for making your own bologna, snack sticks and thawinging meat out for it. I make 20# of one or two recipes for the smokehouse and it would never fit in the kitchen fridge.