Oh...sorry...sorry...I just glanced through your post and didn't notice you were asking about paint.

For paint you'd need to get a polish or paint cleaner for paint, both comes in thick liquid form (like liquid wax) and you can use it by hand. A couple of products that comes to mind are Duragloss #501 Marine Polish (AIO) All In One Paint Cleaner+Sealant or Meguiars SwirlX. If you're looking for cheaper options you can try Soft99 Meta Clean. There is one other product that I know of that is a spray and wipe type. I've seen it been used before at one of my friend's detailing centre but I haven't personally use it myself before. It's Duragloss 505 Water Spot Removal.

And for clay, then yes, it might be able to remove the more milder water marks.