How do I handle a thin strip of vinyl plank flooring against a wall?
Most modern vinyl flooring locks together securely, and since you're putting down shoe I'd have no concerns--if the plank can't lift it can't come loose. I recently did my laundry room and had this same issue for part of a wall. It's not always possible to plan away such scenarios. My flooring has no problems.
Don't do anything hacky like larger moldings. That'll look lazy and amateurish. Just stick to the recipe and take care to get as good a bond as possible.