I posted the same question on the Cassette Google Group, and the lead dev (Andrew Davey) reckons the simplest way to achieve this is to wrap the Cassette HTML Helper methods with a helper of your own which strips out the '/cassette.axd/asset/' part of the URL. The query-string hash parameter at the end of the URL is then simply ignored.
As Andrew says, it's a bit of a hack but I'm quite happy to do this when running integration tests.
(The linked Google Group thread also suggests a more elegant path of exploration to achieve this.)