Isn't the whole point of the sunglasses to cover a good portion of her face, to increase the chance of people believing she's a male bodyguard? Nothing more than that. As long as her cover isn't blown, it doesn't really matter what she does. Having a run so early that only a few people, most of all very few students, are awake, probably has proven to be safe without the sunglasses. Showing the elf ears would still be a huge risk, so she covers them with the massive hat. Since those ears would absolutely be one of the most distinctive features of hers, when they can't be seen, few would actually connect the dots, especially if she's not walking next to the princess.