Mark Engstrom of Toronto's Royal Ontario Museum says he'll likely know by Tuesday whether his team can take it on as well.
It's believed the two whales are among nine that were crushed or drowned in heavy sea ice earlier this spring.
The museum is labelling each bone and preserving samples that will be trucked to Ontario and later available to global scientists.
Local officials had asked for help to deal with the huge carcasses after the federal government said it wasn't responsible.
Engstrom says he had hoped to dismember both whales but it's a massive job that has cost more than expected.
He expects to finish work on the first whale on schedule Tuesday, five days after work began.