Heels would probably be a very bad idea. If you're in a park, you'll be doing a LOT of walking. I don't remember what orientation is like at a resort. Unless you're used to walking on uneven surfaces (mostly concrete), going up and down stairs, and being in said heels for hours, I wouldn't do it. I'd recommend you get a cheap pair of cute flats from Payless or something and break them in before you leave.
Check-in is casual. I have a visible tattoo and it showed at check-in, with no problems. Leather shoes for Traditions and orientation, yes. I don't remember what shoes MK merchandise wears, but they'll let you know when you get there

It's probably black leather or athletic shoes, though.