We can indeed see Orion naked. Fortunately, he's an easier one.
For Orion, you only need two things: High charisma, and get lost before orientation.
You can actually just follow the Silas guide, with two exceptions. First, choose "Love" as what you desire instead of "Knowledge". This gives charisma. Second, when you are at the tent scene and select "Cuddle with Silas", choose to make Silas the "Little spoon". This grants more charisma than making him the big spoon.
By the way, in the Silas guide the route I gave gives more intelligence than is actually necessary, so with the first change you can still see Silas before getting Orion.
The next choice after you finish the altered Silas path should be Silas offering a tour at the academy. Neither choice here matters, though I recommend accepting.
If you didn't give Silas your last name in the carriage ride, you'll get to make one when you talk to the woman at the admin office. Once you finish with her, you'll get to try to navigate the halls on your own. Do so incorrectly by only choosing "Right" and you'll be lost in no time and successfully find Orion in a towel.
Orion will take you to his room so he can change. When he asks you to turn around, choose "Don't". This option only appears if you have high enough charisma. He'll ask again, to which you should choose "Don't". Orion will then lower his towel and his opinion of you, so maybe not the right choice if you want to be his best friend.