You've chosen the one option that will give people a close up look, the pegasus riders. And while it's possible word will get out, it is far from a certainty yet.
As for travel time, traveling day and night will take us from 10-12 hours of travel time (depending on the time of year) to 16 hours of travel time, ish.
If Ryza averages 40mph and has to rest half of her travel time hours, that means she can travel 20 miles per hour of travel time on average, and she has to travel roughly 425 miles. That's a total of 21.25 hours of travel time to arrive at her destination.
It's presently dusk. Let's say there are 10 or so sufficiently dark hours for night travel. Traveling at night, they will get there in two nights and a little change, or roughly 34 hours. (They'll have to make the end of the journey on foot anyway, it's not like Ryza can land as a dragon in the courtyard of the Duke's castle without anyone noticing. They'll have to land out of sight a few miles out of town somewhere.)
Traveling during the day they'll get (16 * 20) 320 miles the first night and day, then they'll need a rest during daylight, then they'll finish the journey after another 5.25 hours of travel time, arriving after a total of 29.25 hours.
If they push through and Ryza is capable of sleeping during the 50% downtimes, they could do it in 21.25 hours, arriving in the evening.
So it's really not an enormous difference. Thirteen hours at most, using rough estimates. Probably less. Compared to weeks it'll probably take to gather and march troops.