How many grams of whale meat is it safe to feed my cat in a week?

I would limit the intake of whale meat due to possible contamination of whales killed in Norway, according to Japanese findings. They tested for organochloride pesticides (dieldrin and aldrin) and bacterial contamination (not specified). Both dieldrin and aldrin have been banned. Dieldrin stays in the body a long time if ingested, and aldrin is converted to dieldrin. So it's easy to see where animals higher up the food chain (such as sharks & fish-eating whales) will concentrate dieldrin as it eats contaminated animals. Minke sometimes eat small fish and crustaceans which feed on other sea life. Mercury similarly can become concentrated in ocean animals from the same effect, although it is more concentrated in the liver.

An older Japanese study considers whale meat consumption of .1 grams per person per day as low consumption and presumably low risk of mercury and organochlorine. You'd have to convert the size of your cat and scale down, but 50g a week seems to be on the high end.

If you do continue to feed whale meat, avoid organ meats and tails which have more fat, and do so less often or at lower quantity.

Sources: https://eia-international.org/wp-content/uploads/Recent-Cases-of-Violation-of-the-Food-Sanitation-Laws-Whale-Meat-.pdf (Pesticides & bacterial contamination) https://www.atsdr.cdc.gov/phs/phs.asp?id=315&tid=56 (Health risks of specific organochloride pesticides) http://palumbi.stanford.edu/manuscripts/Simmonds%20et%20al%202002.pdf (Consumption of whale meat)