Can I leave out raw already-formed cookies for close to an hour while I wait for the oven to be available?
You're going to have more issues with cookie-spreading than anything else, because your fat is going to get all warm. If you have a lot of fat in your cookies, you're definitely going to want to put the dough back in the fridge. If the dough is a hard dough, and you don't expect your cookies to significantly change shape during cooking, I wouldn't worry about it.

There is no concern for spoilage for an hour or less on the counter.