Is it possible to retrieve the player's mouse in a regular script?

It is possible, though this method may become unusable one day. You must use RemoteFunctions. For the server script (whatever name), have the following:

local mouseGet = Game:GetService("ReplicatedStorage"):FindFirstChild("MouseGet") or Instance.new("RemoteFunction", Game:GetService("ReplicatedStorage"))
mouseGet.Name = "MouseGet"
game.Players.PlayerAdded:connect(function(Player)
    local playerMouse
    Player:WaitForChild("PlayerGui"):WaitForChild("MouseGetControl") --Wait for the control script to load.
    repeat playerMouse = mouseGet:InvokeClient(Player) until playerMouse --Get the player's mouse.
    --Do whatever you want.
end)

Now, have a script in the StarterGui called "MouseGetControl":

local mouseGet = Game:GetService("ReplicatedStorage"):FindFirstChild("MouseGet") or Instance.new("RemoteFunction", Game:GetService("ReplicatedStorage"))
mouseGet.Name = "MouseGet"
mouseGet.OnClientInvoke = function()
    return Game.Players.LocalPlayer:GetMouse() --Return the mouse object.
end

This is untested, however I am confident that it will function correctly.