I would not compare "Uruha" with "Kouyou". Uruha is his stage person, you could say a roleplay, it is his profession. He himself said he hates to wear garters and show his legs, but he does it because fans expect it from him. If you noticed, he is very polite- he uses a very polite speech, f.e. when they did their busines cards for the second time (uruha with Kai), when uruha drew his, he showed it to the kamera and sait: "watakushi"- it stands for "me", but it is like...super polite. normally he would use "boku" or "watashi". Not one person and not only fans describe him as shy, thats why I think this part of his personality is true.
You can see he is totally different from Ruki, who is flashy and extreme not only as Ruki, but as a private person as well. Ruki is an artist. That explains much.
Or Aoi- who often makes perverse jokes, not only in twitter, but on his radio show as well....