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I'm planning on teaching one of them Mean Look, Perish Song, Recover, and Softboiled. Combined with the Soundproof ability, my strategy should be obvious. Snorlax has better HP, but Shuckle is all about defense. Which one is more viable? Or is there a better Pokémon for this strategy?

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Are there any Pokemon, moves, or abilities that you're not allowed to use?
There are no Pokémon, moves, or abilities I'm not allowed to use.
Are you allowed to have 252 EVs in every stat?
Unless there's an Action Replay code I don't yet have that allows this, then no.

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252 Atk Deoxys-Attack Zen Headbutt vs. 252 HP / 252+ Def Eviolite Chansey: 222-262 (31.5 - 37.2%) -- 84.9% chance to 3HKO
252 SpA Deoxys-Attack Extrasensory vs. 252 HP / 4 SpD Eviolite Chansey: 108-127 (15.3 - 18%) -- possible 6HKO
Average damage: 25.5%
252 Atk Deoxys-Attack Zen Headbutt vs. 252 HP / 252+ Def Snorlax: 157-186 (29.9 - 35.4%) -- 26.1% chance to 3HKO
252 SpA Deoxys-Attack Extrasensory vs. 252 HP / 4 SpD Snorlax: 154-183 (29.3 - 34.9%) -- 11% chance to 3HKO
Average damage: 32.4%
252 Atk Deoxys-Attack Zen Headbutt vs. 4 HP / 252+ Def Snorlax: 157-186 (33.9 - 40.2%) -- guaranteed 3HKO
252 SpA Deoxys-Attack Extrasensory vs. 4 HP / 252 SpD Snorlax: 124-147 (26.8 - 31.8%) -- guaranteed 4HKO
Average damage: 33.2%
252 Atk Deoxys-Attack Zen Headbutt vs. 252 HP / 228 Def Shuckle: 72-85 (29.5 - 34.8%) -- 10.2% chance to 3HKO
252 SpA Deoxys-Attack Extrasensory vs. 252 HP / 28+ SpD Shuckle: 72-85 (29.5 - 34.8%) -- 10.2% chance to 3HKO
Average damage: 32.2%
252 Atk Deoxys-Attack Zen Headbutt vs. 252 HP / 4 Def Shuckle: 81-96 (33.1 - 39.3%) -- 100% chance to 3HKO
252 SpA Deoxys-Attack Extrasensory vs. 252 HP / 252+ SpD Shuckle: 66-78 (27 - 31.9%) -- guaranteed 4HKO
Average damage: 32.8%
So Chansey is likely the best Pokemon at taking neutrally effective hits, but it has only one resistance. If you want more resistances, use Registeel.
source

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I would go for Snorlax, as even though Shuckle’s defences are through the roof at 230 each, its speed is a dismal 5. Also, Its hp is only 20. Snorlax has 160 hp, and decent defenses. (65 physical Defense and 110 special Defense.) Its speed isn’t the greatest at only 30, but it’s better than Shuckle’s.

Source: https://pokemondb.net/pokedex/all I just searched the names and their stats were there.

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Are you sure Chansey is not better than both of them?
Yes, but I was awnsering whether Snorlax or Shuckle was better, as the question asked
I also asked if there was a better option. The two Pokémon in the question are merely two choices I'm considering. I want the best option out of all Gen 1-5 Pokémon though.
Didn’t notice that, but yeah, Chansey might be better