Originally Posted by
fortnern
I put 20x2.0 Big Apples on my wife's Dahon and they measure more like 1.75, so I don't think you'll have a problem with your rim (especially if 19mm is the internal width). They work great for the type of riding you describe. Mine are the old style Big Apples (HS338), so I can't be sure if Schwalbe changed the sizing with the new version (HS430).
I took this advice and went with Big Apples front and back, with the HS430 tread - they are indeed not far off 1.75" and fitted fine on the rims. Lighter than the 1.75 tyres they replaced too. The puncture protection looks reassuring.