So let's discuss how this would go for Pokemon RSE since that's the one I'm most familiar with.
First off, you can't really take Mudkip. Not only is there the imperfect accuracy issue, Rival 2's Grovyle has only attacking moves meaning that it has to be OHKOed, which without "excessive grinding" isn't possible without a crit. Even going for a crit means relying on Grovyle not going for Quick Attack, something it's fairly liable to do vs Swellow for example. It also can't be Shedinja'd (something that would be an excellent tool).
So we're left with Treecko or Torchic. Treecko, frankly, doesn't have the necessary power to work. It's got the better Roxanne matchup by far but its lower attacking stats and STAB move BP mean that route trainers are a struggle. So we're stuck with Torchic.
Thankfully this also means Rival 1 doesn't have Pound or Scratch, reducing the number of resets.
Torchic is going to want to become a Combusken for Roxanne. While you can OHKO the Geodude(s) with Wingull or something, Nosepass needs a bit more power and Double Kick provides. You'll almost certainly have to reset for either crits or non-attacking moves though.
Brawly is irrelevant since he can be skipped until later to allow for OHKOing.
Rival 2 is a bit tricky but not bad since we took Torchic. We'll want a Geodude to OHKO Slugma (Numel if RS and from now on I'm going to assume Emerald) and evolve a Swellow for Lombre. A Shedinja can hard wall Marshtomp, or it's possible to train an Oddish to a relatively high level and go for a Bullet Seed KO instead. We also probably want to grab an Oddish for Sleep Powder.
Wattson's Voltorb must be OHKOed (all attacking moves) and we'll want to have a way to OHKO Magneton as well since we can't guarantee Shedinja vs it because of Supersonic although that can just be reset through. The game corner can get Combusken Flamethrower. Hope you like gambling. Shedinja handles Electrike and Manectric, but be prepared to have to reset for AI prediction in case they switch.
Maxie 1 isn't too bad. Main thing is getting Combusken (or Blaziken if necessary) to OHKO Mightyena despite Intimidate, either with Double Kick or Flamethrower. Plusle or Manectric or Alakazam should go for the Zubat OHKO (Graveler can work too). Either Tentacool with Bubblebeam (although it's difficult to train) or a Pelipper can go for a Camerupt OHKO. Then they'll need some more training for Flannery - recommend going for Tentacruel to make the Torkoal OHKO easier. Torkoal is the Flannery issue.
Swing by Brawly to OHKO x3 and then Norman. Blaziken is mandatory now - we need to be OHKOing. Shedinja is too risky to use vs Spinda or Linoone due to AI switching. A Protect/Toxic mon (not like Toxic is going to be used otherwise) beats Slaking.
Rival 3 is no thang. OHKO the Lombre with your handy Swellow, rain boost OHKO Slugma with your Flannery killer, and then Shedinja the Marshtomp.
Skip Winona for a while to get levels up naturally to not "overgrind". It's not like we're in a hurry.
Maxie 2 isn't too bad. Mightyena can be either OHKOed or reset for not-Take Down/Swagger not punching yourself. Crobat should be either Alakazamed or Manectric Thunderbolted since it is fast. Camerupt can be watered.
Tate and Liza are somewhat of a trial. Multiple Sharpedo is probably the best bet here. Focus down the Claydol and Solrock, and then use a Flute to keep things unconfused from Xatu. Neither Xatu or Lunatone can do damage to Dark types aside from Xatu's confuse ray.
Double battle Maxie is pray for RNG since you're stuck with Steven. Not much can be done here outside massive leveling with a Wailord to use Water Spout on everything and pray for OHKOs and that Crobat doesn't actually do an attacking move.
Archie is cake comparatively. Just remember to not have Blaziken Double Kick the Sharpedo and take rough skin damage.
Juan is also incredibly easy, just OHKO the Luvdisc with a good electric type and then throw Shedinja at the rest.
Wally isn't bad at all. Ice Beam the Altaria with Wailord or something, Brick Break the Delcatty, Flamethrower the Roselia and Magneton, and have Sharpedo or some other Dark type take out Gardevoir.
I'm going to say the league is possible but absolutely god awful. First, the not so bad.
Sidney can be 6-0ed by Blaziken Brick Break after a teammate OHKOs (or eats Sand Attack and 2HKOs) Mightyena so no Intimidate.
Glacia will require either a very high leveled Blaziken, one that's got a good Attack stat through nature, IVs, and EVs, or a crit on Walrein in order to Blaziken sweep. It's theoretically plausible to have a Magneton Thunder KO Walrein as well, although that'll also certainly take a bunch of levels.
Drake is liable to take a few tries in order to abuse him switching out of Kingdra vs Shedinja so that Ice Beam can KO his team. It's also possible to maybe train up a Salamence to the point where it can OHKO everything with Dragon Claw.
And the unlikely at best.
Wallace thankfully has three Pokemon walled by Shedinja. Unfortunately, one of the Pokemon that isn't walled is Milotic, who OHKOing is unlikely to say the least. Manipulating it into using Recover on the first turn will also take a long time and doesn't even really help since that just means it gets to heal some. It needs to sleep. Getting a Vileplume up to outspeed Milotic requires a lot of levels to say the least, and Sleep Powder's accuracy isn't perfect, so that'll require resets more than likely. Breloom can outspeed without too too much issue, but that requires training up a Shroomish to level 54 before evolving. Without it being able to take damage. That will take an age and a half, and Breloom doesn't even have a great chance of actually managing the KO during the sleep turns, partly because of Marvel Scale. Gardevoir is probably the best option, but even then has to contend with Hypnosis' poor accuracy and is very likely to incite Wallace to use a Full Restore in the course of trying to kill Milotic, meaning it has to hit again.
The other option from sleep is OHKO moves. There's two viable options honestly, since everything else is on the sluggish side (although Seaking could work if you're determined). Glalie (base 80, learns Sheer Cold at 61) and Pinsir (base 85, learns Guillotine at 37). This obviously requires a lot of luck, especially if the goal is to take out all of the Pokemon who can beat Shedinja. In other words, a lot of resets again.
Phoebe is similar, with difficulty in OHKOing her Sableye or Dusclops without critting, but she's notable because Dusclops 2 has only attacking moves, so no way to get maybe bailed out. She's also immune to Guillotine so no cheesing like that.
Final summary: way, way too much resetting and grinding up random Pokemon for my tastes. It also wouldn't be particularly interesting to watch imo because either it'd be dreadfully boring (so many resets to show) or not particularly exciting as you have to luck your way past so many Pokemon.
