How about having this discussion in the preliminary emails? Take the card too, but let them know in advance so it is less of a surprise at interview time.
The interviewers will (hopefully!) be told what time the interview is, so this information could be forwarded at the same time.
And if the HR team can't ensure the interviewers have this extremely relevant piece of information? That's probably a signal about how effectively that company handles communication.
I have two friends who stutter, and it never occurred to me that their condition could be worth mentioning[0]. Maybe it isn't as bad as OP's, though.
[0] Unless one goes for an acting career, of course. On a serious note—I know it's easier to say, but maybe it would help OP stammer less if he didn't perceive it as something of importance in his professional area.
All I can say, I had an interaction today that reinforced my view. Was at a friend's house and her boyfriend announced at the beginning of lunch, "Please just know I have severe hearing problems, so if I don't respond or continue a conversation we're not actually having, it's not you or me being rude, please just correct me." I really appreciated him being honest and upfront and it enables me to better cater the conversation to suit his needs as we spoke. I recognize that a studder is different in that the interviewer doesn't have to adjust his way of speaking but rather his listening, but I still think there's a benefit from the heads up. Maybe just say so instead of giving a card, then.