Other winter squashes can be used here in place of the delicata. Squashes with edible, thin skin like kabocha or kuri squash are great for this recipe, since they don't have to be peeled, and the skin gets crispy in the oven. You can use tough skinned squashes like butternut as well, just make sure to peel them first.
If you don't have a cast iron skillet, you can saute the onions and chard in a regular skillet, then assemble the gratin in a baking dish of a similar size.