Transport Strike Cheese Sauce (i.e. no milk in my town)

So as those of you here in Morocco know, there was a transit strike over the last week. This means that there is no milk in my town. I had a recipe for cheese sauce and some Swiss cheese I found awhile back when I was traveling through Ouarzazate. The recipe, by the way, was copied from Kevin and Kimberly Stout (which I copied when I was up in Germany for Christmas).

Here's my modified version:

4 Tbsp butter
4 Tbsp flour
1/2 tsp salt (plus a little more to add to taste)
1/4 tsp pepper
2 cups water
7 triangles laughing cow cheese(i.e. vache qui rit)
1 1/2 tsp Worcestershire sauce
2 cups grated cheese of your choice (pcv's will probably use Red Ball which I think would work well though like I said, I found some "fromage emmental" or something like that- same as swiss cheese which was fabulous)

Start by melting the butter on low heat in a sauce pan... mix in the flour, salt and pepper with a whisk. Add 2 cups water and bring up to temperature so it's close to a boil adding the laughing cow cheese triangles and whisking in till it's mixed in the water. When the water is really hot and nearly boiling, add the grated cheese, worcestershire sauce and stir constantly until sauce is relatively thick (it will thicken as it cools as well so a good way to tell is as your stir, is it sticking just a little to the sides of the sauce pan before running down into the pot slowly?)

Taste it- I added a large pinch more salt to mine to bring out the flavor but this probably depends on the cheese. If it tastes awesome and looks done, then you're finished.

The unmodified recipe uses milk instead of the water and laughing cow cheese and I've had it... it's also delicious. (2 cups milk in my recipe) My version was also cut down by 1/3 from the original due to the quantity of cheese I had.

Cheers!