Placing it on cardboard should be OK, but putting it on the anti-static bag which it shipped in would be better.
Never operate electronics on an anti-static surface. The "Anit-static" part of the surface is conductive. You may short-out your electronics. That is what makes it anit-static, the ability to allow electricity to ground-out and flow freely through the material.
I suggest an insulated material, like plastic, or at-least dry wood. (Milk crate, sheet of plywood, clean unrolled soda-bottle, even wax-paper is fine.) Not styrofoam which is static-generating, or anti-static plastic, which is semi-conductive.
Yes the cards are fine used without risers, as long as they are supported. They are too heavy to free-stand, and may crack the mobo or pull/stress the pci-e connections. For safety, use a ground-wire attached to one of the mobo-mounting-holes, going to the PSU, and also to each of the cards metal mounting brackets. (Though, honestly, there are enough ground connections through the ground-wires.)
You should be fine.
