Don't know how similar Aussie law is to Canadian, but in Canada there is provision for a pardon of criminal offenses once two years have elapsed since the end of whatever the penalty was for the offense. (Assuming you've been a good boy, of course.)
This doesn't actually remove the conviction, but it does remove the record of it so thoroughly from the general police records that a search by anything not requiring a court order will NOT uncover it. So then it simply becomes a matter of conscience whether to admit it or not....you know, take the same moral high road with CX that CX always takes with their employees...(pardon, is my sarcasm showing?)
'Course could be moot depending on the workings of the Antipodean legal system. But good luck.