The WUR is a "dumb" device that works from a 12 volt source heating a bi-metal that alters the output "control pressure" getting to the top chamber of the FD (Fuel Distributor).
The system pressure lives in the bottom chamber of the fuel distributor. The control pressure lives in the top chamber of the fuel distributor and is controlled by the WUR. The fuel metering plunger lives between the two pressures in its own silo like chamber.
When you first start the engine the WUR provides low fuel pressure to the top chamber (top of the fuel metering plunger) which allows the fuel metering plunger to ride higher in it's chamber thus allowing more of the fuel metering slots to be exposed which results in a mixture enrichment. As the WUR bi-metal heats from the 12 volts supplied to the WUR it slowly raises the "control pressure" (pressure in the top chamber) which forces the fuel metering plunger lower in it's chamber thus exposing less of the fuel metering slots which in turn makes the mixture leaner.
If you suspect the WUR then your first step should have been to check the control pressure. If the WUR is doing its job, then on initial start from cold, the control pressure should be around 20 psi. As the WUR heats (not the engine but the bi-metal in the WUR) it increases the control pressure to somewhere in the area of 50 psi (maybe even 60psi). If those are the results you get when checking the control pressure (checked at the top of the FD) then the WUR is doing it's job and need not be replaced.
The WUR is not to be confused with the cold start valve which is actually just a 9th injector that pours raw gas into the intake when the engine coolant temperature is below a certain value.
Before you start changing more parts, check the system pressure and the control pressure. If you need advice on how to do that just ask... there are many here who will show you how. If both the system pressure and the control pressure check out then it's time to look elsewhere for your problem. There are many things that can cause your symptoms, so we need to take each one in it's turn.