LB: “One Shabbat, attended a shiur about Ashair Yatzar at the shul. The rabbi said that negel vasser is not required, ever. All that is required is to wash hands with water before saying Ashair Yatzar.”
I think you must have misunderstood what he meant LB. There is definitely an obligation to wash negelvasser in the morning. You definitely have to pour water over each hand 3 times.
You are supposed to use a cup but if you can’t, you have still fulfilled your obligation. Maybe, that’s what he meant – that if you don’t have a cup, it’s ok (although it’s better to use a cup).
Until you pour water over each hand 3 hands, your hands have a ruach ra’ah and you are not allowed to touch any openings in your body until you do this, so using the bathroom could be a problem. You are also not allowed to touch food before you pour water over each hand 3 times.