Can I run a plumbing vent through a wall instead of the roof?
You will need some kind of vent or the gasses will end up inside the house. In my jurisdiction tiny homes follow very similar rules to standard construction so a minimum of 1 vent will be needed. A second vent could be achieved by using an air admittance valve if allowed in your area. 

I wired a mobile home not long ago and the owner had his vent on the trailing wall below the ridge. We passed electrical and I did not notice any plumbing changes so that may be an option. I would verify with your local inspector.