The breezer uptown is more upright than a typical British 3 speed. The old British light roadsters basically have the tops of the handlebars level with the top of the seat.

You can adapt an old three speed by using a longer stem if you need to be more upright than that. I have an 11" stem on my grocery-getter/beater:


And I still have about 3" of height I'm not using.

I don't know why you want to have no weight on your hands for, but I personally need to be leaned even just a tad forward to save my butt and back. The grips I'm using on that bike allow me to grab the handlebars by the ends if I want to sit completely upright, but I generally do not ride like that.