Searching for old share market transactions

Can ASX share transactions dating back to 2002 be traced without a HIN or broker details?

Scenario:  

An ex-trustee of a family trust and former director of a company is believed to have purchased and sold shares in ASX-listed companies. A request for records has been made but not responded to.

Is it possible to request records from organisations such as the ASX, ASIC, or share registries without a HIN or knowledge of the broker?

Thanks in anticipation