Andrew. Yes it can run quite adequately on one prop and this is by far the simplest way to go.
I would allow a generous prop clearance, to fit a prop up to at least 60mm to give you lee-way in prop choice (not suggesting a 60mm prop is whats wanted, but leave your options open)
Likewise, a 5mm diameter propshaft is my suggestion, especially as likely your propshaft will be quite long, and I am wary that 4mm diameter long shafts may flex and vibrate. usually the motor is fitted well forward, to give a shallow propshaft angle, unless the drawings give or suggest a position.
Do some surfing regarding brushless motor choice, as this is a right minefield, assuming there are no suggestions forthcoming on this forum.
Probably a large 800-900Kv outrunner will be required, running on a 12V Nimh Battery pack. Off the top of my head, something in excess of at least 150W will be needed and more likely 200+W…so look for motors needing a 30-50A ESC. No doubt someone who has built something similar and fitted a brushless motor will put me straight.
Ashley