It's pronounced like "cock". It's named after the animal, and that's how you say it in French. It's how people who use the tool say it.
(edit: maybe you're English? Some English accents of England would articulate "cock" very close to French "coq" and "joke" would be far away. Apologies, one really does need to specify which "English" is meant, and I should have seen that at once. First cup of coffee still in progress.)
In your example the 'o' is more precise and the 'k' is swallowed a little.
I'd expect they're different accents, perhaps your example is more Northern French (I really don't know).