What's the best way to change a player body when they load?

In my game, I want the player to be two cute little blocks on top of each other, so I've tried this:

wait()
player = game.Players.LocalPlayer.Character
player.Humanoid.WalkSpeed = 23
player.Head.face:Destroy()
parts = player:GetChildren()
for i, v in pairs(parts) do
	if i < 7 then
		v.Transparency = 1
	end
end
body = game.Lighting.Body:Clone()
body.Parent = game.Workspace
while wait() do
	body:SetPrimaryPartCFrame(player.Torso.CFrame)
end

(with body being the model which I want the player to look like) Though because of this, player movement looks very strange because it keeps teleporting the body to the player, though I don't know any alternative! What's the best way to make every player have this body but still have movement be smooth? Thanks!