There currently in nothing else in the shop to vent to. I am planning on putting in a bathroom sometime later on tho. As far as where it will drain to, I will prolly just run it out into the woods. Its a common practise in this area to run gray water like that if you have enough property for it not to be a nucience to any other neighbors. No problem for me as it's a several hundred feet in any direction to my property line and 1/2 mile to the next house. When I get the bathroom installed I can always hook it into the sewer at that time if I decide I don't like it running into the woods. However, that is unlikely that I will as I work away for several months at a time and have had the water evaporate out of the trap before and allow sewer gas into the building. Not fun.
By cheater vent I assume yall mean a short vent stubbed up into the wall? If so, that is what I will do.