The risk really wasn't all that great. Without the geass power, Lelouch never would've met Cornelia or Kirihara or any of the others that recognized Lelouch (Clovas, Euphy, etc...). Cornelia because Clovas would've stayed alive so there would've been no need for her to become Viceroy. Kirihara because he wouldn't have needed to meet with the 6 head families, remember he only meets Kirihara/reveals his identity to secure support for the Black Knights.
While they lived at a school for Brittanians, Brittania is very caste based, and the castes don't mix much, besides a few outliers like Euphy the royal family doesn't mingle with commoners. Which is what the Knights of the Round call Ashford Academy when they transfer to it. So no real chance of running into someone who would recognize them there.
As for those few - and it was very few - Japanese who knew their secret, they also all knew that he hates the empire and why he was exiled to Japan in the first place. So they are far more likely, if they ever ran into him, to support him and hide him from the Brittanians then to out him. As can be seen by Kirihara immediately throwing his support behind Zero when he learns that Zero is Lelouch.
Finally: (This block doesn't actually effect Lelouch's decision to be in public since it's not known to him at the time, but it's interesting to note for us viewers, since it explains why they were so safe for the 7 years before Lelouch gets geass.)
At the end of Season 2 we learn that none of Lelouch's siblings were actually after him and his sister and mother when they were younger. In fact from their reactions they all actually seem to miss them. We also learn that the Emperor wasn't after them either and in-fact exiled them to Japan to keep them "safe" from his brother VV. And as far as we know VV wasn't actually hunting them again until CC came into their life and gave geass to Lelouch. So no one in the Empire was actually hunting them at all.