Since if you want to route direct! No need to file from Strathaven to Bute if you keep out of controlled airspace.
(and not allowed in this summer, anyway!)
Was told the tower just put in the XXXXs when you asked for zone transit prior by phone (as they requested at GLA and EDI after assistants were found to be unnecessary!) or the old-fashioned over the radio way.
So didn't seem helpful there not being an ICAO code for Bute (or Strathaven).
Bute is a classic example where if you take annual movements and divide by 365, you won't have much of a daily average. Yet on a nice day it can be busy busy!