Hi,
The class of the body or the iframe cannot be changed as it is added automatically by the popup system.
And you already have specific classes in each view in deeper elements of the popup where HikaShop is adding its HTML.
So if you want to style the upper HTML elements of the popup, you won't be able to discriminate between the two cases like you want.
I see some alternatives:
1. Change the "address selector" setting of the HikaShop configuration to "list" or "dropdown" so that the address interface on the checkout doesn't use a popup.
2. Update to HikaShop 3.2.0. It has a whole new checkout system, without popups for the address edition on the checkout but much better.