There are enough tools in Link's moveset to vary his playstyle a little bit more than just projectile based stuff for certain matchups, but think of Link kind of like Peach in the way that projectiles are a large portion of his metagame. Of course there are matchups where you just are going to have to use projectiles a large portion of the match for zoning and punishes (well known cases are Marth and the three main floaties: Jigglypuff, Peach, and Ice Climbers), but there are other matchups where projectiles are a good portion while not being the only option (mostly the fast fallers: Fox, Falco, and Captain Falcon). Sheik is a combination of both. In terms of the other parts of his neutral game, you seem to have a good idea that the other part of his neutral game that is not based on projectiles is spacing with the sword, similar to Marth (difference being that Marth went for speed instead of the option to fight long-range). But I should tell you about the moves that you listed in terms of their usefulness since your friend plays Fox and I don't know if he's going to put in more work to make himself better. I can tell you right off the bat that your use of Dtilt and Ftilt is going to hurt you in the matchup. Many characters can come in and punish the Ftilt end lag, and Ftilt mostly is used to hit the opponent on the edge with the tip (still very risky) or just very hard reads for kills at high percents. Dtilt is situational as well with its properties, but it still is too slow to pull out freely since it also can be punished (except its the faster characters that can do it this time, and Fox is one of them). Dtilt can lead to aerial followups, but requires a read (not as hard, but still up there). If you want to shield poke him or get a clean hit on his feet, Dsmash is a better move since the hitbox comes out faster (point of notice: if you think that Dsmash isn't going to hit or will be shielded, you shouldn't be using it or Dtilt anyways). My point is that Dtilt and Ftilt are not moves to corner opponents on a regular basis. You already having cornering moves with Nair and Bair, and you already have good approach options with Nair (although Fair is more of a punish/finishing move, maybe pivot Bairs). Also, with the platforms, I would advise to use Uair more for pressure, but FH Nair/Bair has its uses.
So to sum it up, you don't always have to use projectiles depending on the matchup, and his aerials are good for use in the neutral as well. Also, even when his aerials are good (aside from freely used Dair), other lower characters have good aerials as well. What makes Link significantly better aside from projectiles is decent vertical mobility with his FF and he has moves that can string together beautifully for combos. I'm just pointing this out to make sure that the point of good moves doesn't always guarantee good viability in the neutral (Bowser has a beautiful Up B OoS option, but is low in the list for many other reasons.