If SAS casual/athletic shoes are made like most, they should be fine in the rain. I wash my running shoes -- Adidas, Under Armour, etc. -- by dunking them in a bucket of cool/lukewarm water with ordinary laundry soap. Soak for awhile, sponge off or scrub as necessary, air dry. No problems. I wouldn't use hot water or a hot air dryer, though.
And my clipless cycling shoes have been soaked in heavy rain a few times. No problems. While they look like leather, they're all synthetic materials.