Is it a good idea to put on yellow dragon scale mail and go to town with a rubber chicken?

I think you might have gotten some misinformation. Yellow dragon scale mail provides acid resistance, not stoning resistance. In fact, in vanilla Nethack it's not possible to achieve intrinsic or extrinsic stoning resistance at all, aside from polymorphing into a stoning-resistant monster. The confusion might be due to the fact that acidic monsters are useful as a way to prevent stoning (by eating their corpses).

Your idea of wielding a cockatrice corpse as a weapon is not an uncommon strategy, but you need to be wearing gloves at all times and you must be extremely careful, because there are lots of ways that something can go wrong. You may want to wear an amulet of life-saving just to be safe.