It's a little bit of a difficult question to ask, but i will try to explain it:
Yarmulkah seems to come from the Aramaic phrase Yarei Malka (Yirah Melech); fear of the King.
I know the verses of the Talmud like Shabbat 156b and others talking about fear on our heads.
The Kipah on the other hand seems to be connected to Kaf which refers to handpalm but its etymology shows a connection with something bend or bend over in submission.
I also found a possible connection with Choepah: כפה & כפף
The ArtScroll Edition translates Isaiah 9:14 as 'canopy', It reminded me somehow of Chupah, Chupah within Torah is חפה from the root חפף 'which means 'to cover'.
(This is what I found: The word “Chuppah” is based on the root word “chafah,” which means to “cover” or “hide” and is similar to the word “chafaf,” meaning to “protect).
At last i found that Kaf has a gematria of 20 which is 2 times Yod (from Yad meaning hand), which as a word is also 20. When looking at the Kaf it looked like a Kipah on it's side. And it's like the hands(or handpalm) of HaShem is on our head when wearing a Kipah.
Question: If our head-covering is a sign of submission and of awe to our King, than i can see a connection, but there is one link missing for me:
How are the hands of HaShem related with the fear of heaven (Yirah Shamayim or Yirah HaShem)?