The rim sizes are the same for all 20" tires (406), with the exception of a couple of very narrow tires (451).
You say you have about 1/2" of clearance. Your new tire is listed as about 1/20" larger, so you'll probably hardly even notice the size difference, and it could fall within the random variability of tire carcasses from brand to brand.
Anyway, your new tires should be fine.