Another thought just came to mind.
An intermediate proxy could be used to capture and translate cookie data for
httrack. eg.

configure httrack to use intermediate proxy.
proxy captures cookie data on the way out and makes a note1.
proxy captures cookie data on the way in and makes a note2.
when httrack sends the same cookie data back out, the proxy notices (note1)
and replaces it with the new data (note2) it captured on the way in. I'm not
sure how it would deal with multiple pages being requested at the same time
however for a single stream it seems viable. Should be invisible to httrack
and webserver.