First of all, I love this idea and I love the Percy Jackson series.
Now down to business, you want to get Ebony sword enchanted with frost damage and soul trap (this resembles his Stygian iron sword). Wear ebony boots and gauntlets and either black robes or ebony armor enchanted however you like. Alternatively you can skip the Ebony armor altogether and get the Nightingale armor.
Complete the College of Winterhold quest line. Possibly the Thieves guild quest line. You also might want to do some Daedric quests to obtain certain artifacts like: the Ebony Mail, and Mehrunes Razor, those aren't a necessity, just what I would do.
Be proficient in the skills: Conjuration, Destruction, Illusion, Sneak, One-handed, the armor type of your choice (heavy or light), and of course Enchanting.
RP: Be a loner. Nico is definitely a loner, so no follower minus your summons. However, he is a hero, not a villain as you mentioned. So, help the greater good, Destroy the Dark Brotherhood, become thane. Blah blah blah... All that jazz. You may have to do dome dirty deeds to get some cool stuff, so just use an a$$h0le for Boethiah's quest馃槆馃槈.
I think this is a really cool idea. I'm no expert but this is what I would do for a Nico play through. Again, sorry for the mountain of words. Hope you don't mind me stealing the idea.