NA Localization:
"It's nice, seeing the commoners' world once in a while. Don't you agree, Sun King?"
"Hm, getting to steer my mount by hand is rather entertaining!"
"Don't make so much commotion. Our disguises may be perfect, but we are drawing a great deal of attention."
It's the duty of a king to be aware of what's going on with the common people. The three of them stand out far too much to claim this foray is conducted incognito, and there's just no chance they get through this without incident...
Fan Translation:
"It is not so bad to see the commoner's world once in a while, isn't that right, Sunny?"
"Un. It also isn't so bad to drive such a vehicle by using only one's hands!"
"Stop making noises! Our disguise is perfect, and yet people are staring at Us strangely!"
It is the duty of a king to know the streets of their land.
Although they were standing out too much for that to be called an 'incognito travel', with their line-up, they wouldn't have been able to finish this trip peacefully anyway...