Is it possible to create a click button without the need for a ClickDetector?

This isn't as hard as you think, but it is completly local.

You can acces the Mouse in a player (local Mouse = LocalPlayer:GetMouse())

Then use Mouse.Button1Down:Connect(function()

We can then check if Mouse.Target is the part you wanted to be the hidden click detector

F.i. if Mouse.Target == game.Workspace.HiddenClickDetector then

Make sure to check if the Target is not nil though! if Mouse.Target then

In the end this would give us:

local Mouse = game.Players.LocalPlayer:GetMouse()
local HiddenDetector = workspace.HiddenClickDetector

Mouse.Button1Down:Connect(function()
	if Mouse.Target then
		if Mouse.Target == HiddenDetector then
			--Do your stuff
		end
	end
end)

Any questions? Add a comment :D

Edit:

Mouse on wiki: http://wiki.roblox.com/index.php?title=API:Class/Mouse&redirect=yes

You could even add a Value inside the part (A boolean value or something) And check if that Instance is inside of the part, May there ever be a user named "HiddenClickDetector".