W B Johnston's Place Names of Scotland suggests that Shira or Shirra may be from Gaelic siòrabh which he translates as 'lasting river'.
My Gaelic dictionary doesn't include siòrabh.
However sìor is listed as meaning 'long-lasting', 'permanent', 'perpetual' etc, and (unusually) is used before the noun it qualifies.
And abhainn is a variant spelling of abhuinn or amhainn, all pronounced AH-v'n, and meaning 'river'.
So I can see that siòrabh might derive from sìor abhainn, and would sound pretty much like 'Shirav'n', so that is one possible derivation.