If I do game.Players.LocalPlayer:GetMouse().Icon = <icon here> then it doesn't change the mouse if it hovers over a button or clicks on a button. I've looked on the wiki for a property of this sort but there seems that there is no hover/click property.
There's an issue with the mouse icon which you can read here.
It states: "If a plugin changes this property when a TextButton is moused over, the actual mouse cursor may not reflect this property properly."
Sorry if this is what you were wanting.