Others, however, said biopsies were risky for dolphin calves and they had proved fatal in the past.
It is understood the contractor to have carried out the biopsy withdrew on September 18 and DoC has no plans to hire someone else.
News that the plan had been abandoned was welcomed by marine mammal campaigners such as Whale and Dolphin Conservation's Gemma McGrath, who said she was "hugely relieved".
The blubber layer of a common dolphin calf was much thinner than that of other larger cetaceans, she said. "There's a lot of risk in taking a biopsy from smaller species. There's no need to risk invasive research when there are other ways to get the same information."
Researchers could find out about Pee-wee's genetics by analysing skin sloughs and faecal matter. Ongoing photo identification would provide information about future mother-calf associations. It was important to understand what was causing the Bay's high calf mortality rate, "But what's the point in risking the death of a calf when that's the very thing they're trying to prevent in the first place?"
Ms McGrath said DoC should have consulted a wider range of marine scientists and all iwi, "not just a select few", before attempting a biopsy.
DoC did not wish to comment for this story.