I think it can be managed. Whales were already hunted for food and most whale species are doing well. The main problem is the whales that are adaptable and manage to survive the hunting are the ones that feed on fish, squid or similar larger animals. Additionally, it requires time for them to grow into adulthood and this translates very slow selective breeding process.
However, there is a type of whale feeding off of everything, including the ones you have listed and still is listed as least concern for being threatened: Minke whale. Additionally, these whales have shorter pregnancy and become adults between 3 to 8 years. If your expedition chooses this whale for its adaptability, they may use them as food source. Here are few information sources: this and this.