Skull has nothing unusual, it is a perfectly matching 1938-1939 style.

Ring is strange because it shows some details that are "questionable".
I'll try to summarize without entering in details.

Starting from the point that has chances to be real (I would never say about a ring that it is 100% original via pictures, because it is not possible!), the ring IMO, even if is dated 1937, was made and awarded in 1938, because:

1) the skull was made in 1938, not before.
2) the runic designs belong to 1939-1938 pattern
3) The "Heilszeichen" runes in the circle, are hand made, so not matching with any of the known patterns. This could be a problem, very hard to explain if you don't know how these rings were made (and I'm sorry, but I really can't explain it here in few words).
4) the Swaz too has no match.


So, IMO the ring stands chances to be real, and, if real, it is one of the absolutely rare existing, with heavily hand modified runes. Usually, as we all know, the hand modifies were mostly made around the leaves and around the runic symbols, but they usually didn't change the original design.