I think I've fixed it. Or, rather, it's fixed itself. Someone on Flickr kindly reminded me that the shutter is supposed to stay cocked until the film is wound on - which my Isolette so far hasn't bothered with. So I wound the winderer, et voila! Shutter quite happily fires once more.
So it now appears that what I thought was "broken" is apparently "mysterious & spontaneous correct function".
This does put me in mind that the Isolette might not be the most reliable of beasts in future - so I might see if I can get someone (perhaps Walchs in Hobarts) to at least give it a once-over. It is, after all, older than my dad - it's probably well overdue for a service of some kind.