How do I make my remote event only happen to a specific player at a specific time?

I am making a script that changes the player model whenever they touch a certain part. How would I make it only happen to the player that touches the part? Right now it just happens to a random person.

local script (attached to part)

script.Parent.Touched:Connect(function()
local plr = game.Players.LocalPlayer
local camera = workspace.CurrentCamera
local rig = game.Workspace.TheBeast
camera.CameraType = "Follow"
camera.CameraSubject = rig.Head
script.Parent.RemoteEvent:FireServer()
end)

Issue: I want to turn a player character, "beast", into a character model. I'm not sure if you need this to resolve the issue but just in case.

Main Script

local dontrepeat
local beast = math.random[1,game.players:GetChildren]
script.Parent.RemoteEvent.OnServerEvent:Connect(function(plr)

local char = plr.Character
local rig = game.Workspace.TheBeast --the model you want to turn into--



if not rig.HumanoidRootPart:FindFirstChild("DontRepeat") then
    plr.Character = rig
end
wait()
if not rig.HumanoidRootPart:FindFirstChild("DontRepeat") then
dontrepeat = Instance.new("Attachment")
dontrepeat.Name = "DontRepeat"
dontrepeat.Parent = rig.HumanoidRootPart
wait()
char:Destroy()
end
end)