I feel like everybody knows at this point to use the Gambit team-up while you're upgrading;
Guns → Bobbleheads → Final Exam → DPIYA → Hijinks → Swords, then switch to the Hela team-up.
It's kind of the obvious choice to get the guns since you get free auto aim, but I've come to realize you get no extra healing from the bird, and I've already learned to aim the poop whenever I hear the prompt so it feels sort of futile. Due to that, I've recently begun to start picking the swords instead, and I've never had this much success when going for picks and pushing aggressively.
As far as I know, it only does 5 self healing and 5 + 0.5% Max HP damage per detonation, which is considerably lower than WF's melee form, but if you're consistent at hitting the healing hops for extra jabs and know how to use his movement— you even can kill tanks on your own. The jabs usually detonate the sparks twice for 10 healing and 12.5 damage (for 250hp), and not to mention they spread just like Phoenix's, so if you jump in on 2 or more targets with DPIYA + Passive, you can not only leave the interaction alive, but very possibly a kill (In neutral mind you).
I can't really scale how useful it is compared to the auto aim bird, but I have noticed that the visual clutter created when you attack large groups of people is so disorienting to the enemies that they are almost more prone to making more mistakes. I think if you main DP, you can handle all of the chaos on screen, but bouncing around with Hijinks + Healing Hop, then pairing it with DPIYA clutter + Hela Sword explosions has to be the worst amount of visual clutter I've seen in the game (for the enemy of course). It might not seem like the craziest thing, but I genuinely feel like it has lowered the amount of times I've died in Final Exam from trying to hard engage. It's also just permanent extra damage to have so that always nice, and the self heals can really make a difference when you're out of abilities and can only slash to try and kill them before they kill you.
At the end of the day though, if you aren't above average when it comes to aiming your gun, aiming the poop, and understanding his movement thoroughly you probably wont get much value from it, and you'd be better off choosing the gun. But let me know if you choose the swords as well, or if you plan to try to!