not a Williams sprocket, it is a Williams chainring.
That Campagnolo GS RD is for a 5 speed freewheel using a 3/32" chain.

I am unsure of your reference to a "correct type 3/16"
A 3/16" chainring is going to require a 3/16" chain and I don't think that would go through the RD.
And I don't ever recall a 3/16" multispeed freewheel in the 1950s.
This is from Holdsworth's Aids in 1955 from the V-CC Library.



It will be interesting to see if you can use the limit screws to restrict the derailleur to the 4 speed freewheel range.