Alright, Arcanine and Toucannon are your biggest assets here. Next would be Gastly (but fully evolved into Gengar), Primarina, Cottonee, and Sylveon. I'll explain how each would be useful, as well as some general tips:
If your Arcanine has Intimidate then Mimikyu will be significantly easier because all of Mimikyu's attacks are physical. Fire Fang is your best move, because of its chance to Burn. A Burned Mimikyu is a dead Mimikyu. Alternatively, Fire Blast can be used for lots of power, or Will-o-Wisp for direct Burns. (Please note, I don't remember when you get the Will-o-Wisp TM in game, so you might not have it yet.) Also remember that Mimikyu has a Lum Berry, so you'll have to status it twice.
Not only is Toucannon immune to Shadow Claw, it has two moves that are very good at combatting Mimikyu. The first is Pluck. Pluck lets you both break Disguise and steal Mimikyu's Lum Berry. Next is Beak Blast. The way Beak Blast works is, if the opponent makes contact on the turn you use it, they get a Burn. This is perfect because the only move Mimikyu can damage you with, Play Rough, is a contact move! Even if it KOs Toucannon it will still get burned, and if not, it gets dealt a hefty blow by Beak Blast. Plus, if you've already used Pluck, its Lum Berry is gone, so the Burn will stick!
Shadow Balls from a Gengar (or even Haunter) will dent Mimikyu, even if you only get one off before being KOd.
Primarina has several good assets. First, she's bulky enough to probably take a Shadow Claw or Play Rough. Second, she has some good moves at her disposal. Baby-Doll Eyes is a priority move that lowers Mimikyu's Attack. Sing lets you buy some time — if you're lucky, and if Lum Berry is gone. Encore locks Mimikyu into Mimic or Pain Split. She also learns Shadow Ball, but I don't know if you have access to this TM yet. Finally, a Oceanic Operatta will do a lot of damage to Mimikyu, maybe even KOing it, and giving Primarina a Mystic Water will make it even more lethal. I do, however, have one important disclaimer. Do not use Sparkling Aria on Mimikyu if Mimikyu is Burned. It will lose the burn and go back to wrecking your face.
Really only useful if it knows Baby-Doll Eyes.
Cottonee should only be used if it has Prankster. Prankster lets you use Toxic, Stun Spore, Charm, or even Leech Seed on Mimikyu before it can strike. If Cottonee does not have Prankster, then only use it as a sacrifice for reviving a teammate.
Stock up on Hyper Potions and Revives, just in case. Make Mimikyu your priority, but remember that Haunter and Gengar can still do a lot of damage with Shadow Ball or disrupt your plans with Hypnosis. I would recommend getting all of your Pokémon up to or around Mimikyu's level — 32 or 33. And finally, don't be discouraged if it takes you a few tries to beat the Totem. Lurantis took me 5 or 6 tries. Just keep persevering!