Translation:A knife, please.
Yeah, this bothers me too. I was always taught thatください (下さい) is "please". In this context it is how to ask for something, so you could say it has the same literal meaning as "can I get", but that feels more casual than ください. I've noticed they'll swap between between formal and more casual versions of a phrase and give it the same English translation. That's not "wrong", per se, but I really wish they'd let you know which version is which. Being informal in English can be perceived as friendly and approachable, but in Japanese it's much easier for it to be seen as disrespectful (or overly familiar).
The counter word for knife is 丁, so it would be「ナイフを一丁ください」。You can also use 本。