If the big 3 rain sweepers are banned for whatever reason (Kingdra/Kabutops/Ludicolo) then there are a few Swift Swimmers that can replace them.
Floatzel: Seriously underrated. Fastest Swift Swimmer and still outruns most things outside of rain that don't double speed. Able to Bulk Up and either pass and/or attack. 105 base attack is pretty good and has Waterfall/Crunch/Ice Fang/Brick Break. Waterfall does massive damage to Landlos, Doryuzu, and Gliscor and ohkoes the first two without rain (and is faster)and can ohko offensive Gliscor and almost ohko defensive Gliscors after a Bulk Up with Life Orb even without rain. With Adamant Nature and Focus Punch, it can 1-Shot Nattorei with Focus Punch if it switches in if it is max hp/mind def (and kill it with another move if it has defense). Focus Punch is situational but it can work since usually Nattorei would probably never hesitate to switch in on Floatzel (I don't know, Floatzel is a rare Pokemon and who would expect it to pull of a random Focus Punch?). Brick Break will also deal enough that Nattorei is going to be pretty weak against another Swift Swimmer. Burungeru is handled by Crunch and even with Floatzel's shit special defense Burungeru is not particularly threatening to it while after Bulk Up, Life Orb Crunch does over 90% to max hp/~200ish defense Burungeru (max hp/max defense still takes over 70 and is 2 hit koed).
Qwilfish: Fastest Destiny Bond in the game in rain outside Custap Berry. Swords Dance to boost it's attacks and it isn't terrible. Resistances to common priority Mach Punch/Bullet Punch and okayish defenses means it isn't afraid of priority users usually (except maybe stabbed Sucker Punches and potentially Toxicroak although Sucker Punch is only a 2 hit ko). Poison may be a meh attacking type but it smashes grass pokes not Nattorei and the chance of inflicting Toxic type damage is pretty awesome. And it clears Toxic Spikes! Return can go over D-Bond if you really need to hit Toxicroak and it doesn't really have many attacking options really. Maybe Explosion or Thunderwave (what you want to be paralyzing instead of attacking I don't know).
Gorebyss/Omastar: Shell Break is deadly and Gorebyss can Baton Pass it. And behind Screens, it is DEADLY. If priority is your only way to stop it and it is behind screen, you're dead. If Nattorei is your only way to stop it, you're dead once Nattorei is gone or Nattorei is weakened and they pull off Shell Break. While it is a bit more support than expected, it isn't super super hard to pull of a screen and few use Brick Brick and behind Screen, Gorebyss can eat Power Whip from standard (non attack boosting Nattorei) with half it's health left (and still has about 30 after -1) and take less than half from Breloom Mach Punch...-1. Omastar isn't quite as good at Shell Breaking (can't pass, can't take priority nearly as well without Screen, etc) but it might be useful for other things as well and as a just straight out attacker or something. And you could also pull off double shell breaking where one weakens the team and then all of a sudden you pull off a second one and win when their counters are so weak, they can't take a second one (it is hard to take one, let alone two if they manage the time and -1 def without dying).
Poliwrath: Swift Swim Poliwrath is pretty anti Tyranitar. It can use Bulk Up or Belly Drum (feel the terror of Swift Swim Poliwrath. Without Ditto or something faster, you are just kerplunkered dead). It keeps Tyranitar wary of switching in and Nattorei isn't too thrilled either because after a Bulk Up, Brick Break is doing lots of damage, enough to put in kill range of something else and if it's carrying Life Orb and just a tiny bit other damage, can be ohkoed if it's min def after Bulk Up. Belly Drum obviously wins. He's fast and can do Sub Punch and Sub Bulk Up or SubBulkPunch which hurts. It can also use the shaky Hypnosis to attempt to put something to sleep which can be useful if it hits.
Tsunbea: It's an...Ice type and can beat Nattorei with Swords Dance Super Power and is pretty strong. Fighting weakness stinks and it isn't particularly defensive or able to take advantage of a water stab but beating Nattorei, Birijion, Toxicroak, etc is cool.
Still, I'd rather ban permanent weather than Kingdra/Kabutops/Ludicolo (they aren't THAT good to be banned from OU although Kingdra and Ludicolo can have niches in Uber and maybe, maybe Kabutops). But Rain still remains a fairly strong competitor. The existence of Swift Swim Poliwrath however does raise some concerns...