Making crêpes on teflon-coated cookware makes it possible to fold the fat (butter, ..) inside the mixture, and to use no fat while cooking. But some may want to avoid teflon, perhaps for health reasons, perhaps because they're partial to cast iron, etc. For any surface other than teflon (stainless steel, cast iron, ...) applying fat before pouring the crêpe mixture becomes necessary.
What are these two tools? Are these tools accessible to the home cook? Are there substitutes that the home cook can use?
In the first (and other videos) I've seen what looks like an oiled paper towel. If the pan is already at medium heat (and adequately preheated), an oiled paper towel would surely burn quite quickly (not to mention possibly leave lint). Likewise any towel would burn.
The tool used in the second video seems to be some kind of aluminum-covered spreader, but it's unclear whether the handle contains fat or the instrument was simply sitting in a plate of fat.