Is there any relation?
The etymology of English "shade" (newest to oldest) is something like:
- Modern English "shade"
- Old English sċeadu (shadow)
- Proto-Germanic *skađwaz (shadow)
- Proto-Indo-European *sk(e)h₃-tos (darkness)
There's decent evidence for this being a native Indo-European root; while it was most productive in Germanic, it has descendants in different parts of the world as well (Ancient Greek σκότος/skótos, Irish scáth, loaned into Finnish katve).
The main etymology of Hebrew šed that I've found is:
- Modern Hebrew šed (spirit)
- Aramaic šēḏā (demon)
- Akkadian šēdu (a male lamassu (protective zodiac deity))
- (Unknown preceding Proto-Semitic form - but see fdb's answer)
(Transcribing all of these because my computer does not like changing text direction mid-line.)
There doesn't seem to be any obvious connection between *sk(e)h₃-tos and šēdu, in form or in meaning. This is more likely just a coincidence.
Akkadian šēdu is probably cognate with Arabic saʽd “happiness”. Aramaic šēδā and Hebrew šēδ are most probably borrowings from Akkadian, with reversal of the meaning (“good spirit” > “pagan god” > “evil spirit”).The proto-Semitic form would then be *s1aʽd.