4” schedule 40 drain and Pipe and run it out far enough to no be a problem. Perhaps in an area you can use as a compost spot. If the ground will perk use perforated pipe and hose water through it on occasion. I am going to build a processing room outdoors but our house is right on the edge of one of the big hollow that runs through our place so I am just going to pipe it off into there...
I just built a barn where we do our processing. I built an overhang over the apron on one and put a hoist for deer. The apron slants slightly away from the barn. I don't field dress as I've got an ATV and UTV for deer retrieval. I eviscerate deer while hanging. I place a small rubbermaid type tub between the legs to collect viscera. I burry this along with the head, hide, and lower legs to avoid attracting coyotes.
I have reach-in cooler where I hang quarters for aging. We do our processing in the barn right next to that door (overhead type). I have a double tub utility sink near that door. We have mobile tables we setup to do the butchering. When done, I just use a power washer to wash everything out the door on to the apron and then off the apron.
There is so little debris and it is so watered down, we get no smell or have any issues. We did not try to put a drain in the floor. The barn is insulated but not heated. We live in zone 7A, so it is usually not that cold when we process.