This is tough, since Nakamura can't really talk, but there's one thing both men can do. WRESTLE. So, I'm going to try to turn this into a wrestling build-up and also use someof Nakamura's charisma.
First things first, you need to make this match equal to the other two main events, which might end up being: Undertaker vs Cena and Roman vs Lesnar, plus there's a Triple H match on the card. Styles vs Nakamura needs to feel like a big deal. Putting Cena on RAW's elimination chamber was a mistake. They should have booked a John Cena vs Shinsuke Nakamura match at FastLane. But they haven't, so I'll use the other closest superstar to John Cena: Randy Orton.
Have Orton become somewhat heelish for a short feud against Nakamura, which will lead at a match at Fast Lane. Why is that? Well because Nakamura has been booked horribly before his Rumble victory, so we need to pick up the pieces. A victory over a 13-time world champion, before Wrestlemania, can do that, but as I said, having Nakamura beat Cena would have been even better.
So at Fast Lane, Nakamura beats Orton clean and Styles beats Sami and Kevin in a Triple Threat match.
First chapter is done, both Nakamura and Styles have defeated the best talent of Smackdown. Now, onto the build-up.
We have 4 weeks, so they set a bet between them. 4 weeks, 4 different opponents until Wrestlemania. They want to see who will pick up the most victories until then. Each of them will pick the opponent for the other one.
The first week, Nakamura picks Sami Zayn as Styles' opponent and Styles picks Kevin Owens as Nakamura's opponent. Both men win their matches. After the Styles vs Sami match, which goes on last, Owens comes out and they double-team Styles. Nakamura runs out and makes the save. Then, they have a face-off to end the show.
The second week, Nakamura picks Baron Corbin for AJ Styles, but Styles is not so kind, as he picks both KO and Sami Zayn in a handicap match, to face Shinsuke! Nakamura's match is first and Nakamura overcomes the odds as he beats both men (due to interference from Shane McMahon). At the main event Styles is frustated in his match against Corbin and seems distracted. The reason he's frustated is because Nakamura managed to win. Despite all of this, he also manages to pin Corbin, after a brutal match. Post-match Nakamura comes out to congratulate Styles, but Styles, furious that Nakamura won his match with help, declines the hand-shake.
The third week, AJ Styles proposes a Beat the Clock challenge, between them. Styles picks Corbin as Nakamura's opponent, believing that since Corbin was so difficult to defeat, then Nak would also have trouble with him. In the meantime, Nakamura picks Rusev for Styles (all hail Rusev Day!).
So, Nakamura beats Corbin, but Styles was right. It was difficult for Nakamura to do so. At the main event, we have Styles vs Rusev. Styles is overconfident since Nakamura took so long to beat Corbin, and controls most of the match and seems to be going for a very quick victory, however Nakamura decides to make an entrance to support AJ! But instead of that, Nakamura stars having convos with the crowd and panders to the them, which of course takes the crowd completely away from the match. So, he takes AJ's match and turns into something about himself. AJ is distracted by this, which leads to.. Rusev rolling up AJ Styles for the pin! Big upset on Smackdown. Post-match a furious AJ Styles pushes Shinsuke and wants to know what the hell he's doing out here. AJ Styles takes the championships and leaves, shouting that he's the WWE champion, he's the best and stuff. Shinsuke is left in the ring, doing his thing while his music plays.
Before Smackdown goes off-air, Styles does a quick interview saying "I'll show him. He wants to make a fool out of me? I'll show him."
Fourth and final week, the go-home show for Wrestlemania. It's AJ Styles vs Kofi Kingston and Shinsuke Nakamura vs Jinder Mahal & The Sighn Brothers in a 3-on-1 Handicap match. Styles beats Kofi rather quickly via submission. Nakamura wins the match via DQ, since Mahal decides to go for a 3-on-1 beatdown. Styles comes out to make the save this time. After that Styles congratulates Nakamura in an ironic fashion, since Nakamura got a DQ win, a win due to interference and Styles lost a match because he was distracted. Nakamura picks the mic from Styles' hand and says "All.. this.. Children games! Us.. Men. Real man.. walks out Wrestlemania.. WWE Champioooon! AJ, you.. bad loser". And as Nakamura goes to leave, AJ has had enough. He turns Nakamura around and goes for a punch, but hesitates at the last minute. Nakamura screams to him "C'mooon!", however AJ leaves the ring.
But while AJ walks away and the crowd boos, he suddently stops, turns around and rushes to the ring and the two of them start brawling! The locker room comes out to seperate them and Nakamura taunts Styles. Styles picks the belt and goes to Nakamura's face and raises the belt up, while Nak still taunts him.
During the build-up I'd also have backstage skits, featuring Styles and Nakamura in competitive games. Darts, basketball, puzzles, push-ups, board games, chess.. anything you can imagine. This sets up better the fact that Nakamura doesn't really care wether he wins this competition or not. All he cares about is Wrestlemania. Styles is the one that cares about winning this though, because he takes things more seriously.
To sum up: the build-up revolves around Nakamura being a big troll that looks at everything in a funny way and Styles being a bad loser, who looks at things seriously. A healthy competion between two athletes, that quickly turned wild.
After Wrestlemania, they can go in two different ways. AJ turns heel on Nakamura or the two shake hands and hug after their amazing match. I'll have Styles hand the belt to Nakamura, after Nakamura's clean victory. AJ then goes to RAW and Nakamura becomes the face that runs Smackdown.