That's a pretty small area. Water that bounces off the human body and other hard surfaces will most likely splash outside of the shower, could create a slipping hazard when stepping out of the shower. Could work if you have a curb and shower curtain that stays on the inside lip of the curb to catch most of the splashing water. This could allow the over spray to drain properly into the shower vs onto your bathroom floor.

I think it is too small to not have a door. The smallest shower we have done without a door was the size of your whole bathroom. Water splashes so much I would be hesitant to not have a door.

Those shower dimensions seem fine but because of the 46 inch length you'll have water splashing out if you don't do a door.

Why are you trying to avoid a door? I recently re-did my bath and went doorless but the shower length is 72 inches and tiny droplets still splash out. But more falls off of me when I exit the shower. Hard to avoid water drops in a bathroom.

You could get a glass wall + glass door and have no sliding door.

The diagram did not show up for my first comment and now that I see it ... I believe the area is too small to not have a shower door.