Hi EMD!
Yes, that situation works. When you're dealing with Double Not Arrows and thinking about how to combine them with other conditional statements, it is sometimes easier to break the Double Not Arrow into it's component parts, or at least to conceptualize it that way.
W

J breaks down into:
W

-J
and
J

-W
So we can combine W

-J with -J

S and get:
W

-J

S
Take out the middleman and you get:
W

S
That's basically you did and you did it correctly. Just wanted to make sure you were clear on the thought process
Hope this helps!
Best,
Kelsey