How to change default swimming animation?

After copying the Animate script, go back into the game and copy the swimming parts you need. Paste it into the Animate script in StarterCharacterScripts and voila. If this doesn't work, there's a more complex method requiring HumanoidStates. I'll walk you through that if all else fails.

Open up the AnimationScript and scroll down to Line 42 and change the swim ID.

Looks like you don’t need to replace the Animate script entirely, according to the wiki page concerning this, you simply change the AnimationId's value created for the target animation. You will have to refer to the Default Animation Reference prompt to see what the animation is named, here swim.Swim.

local function onCharacterAdded(character)
    local humanoid = character:WaitForChild("Humanoid")

    for _, playingTracks in pairs(humanoid:GetPlayingAnimationTracks()) do
        playingTracks:Stop(0)
    end

    local animateScript = character:WaitForChild("Animate")
    animateScript.swim.Swim.AnimationId = "rbxassetid://123456789"
end

local function onPlayerAdded(player)
    player.CharacterAppearanceLoaded:Connect(onCharacterAdded)
end

Players.PlayerAdded:Connect(onPlayerAdded)