You did not say you actually had a smell, so I am supposing you are looking to prevent a smell that may or may not be there. Your idea of an S-trap sounds functional, but if you really need to isolate smells, then a vent to outdoors would be needed. I would consider not putting in an outside vent unless you develop a smell. But I can see that if there is any doubt, you might want to do it and be done with it.The smell is just a by product
Maybe you will want to pour your old milk or fish-cleaning water down your sink, rather than just washing hands.