I would not give a chin an entire cuttlebone. Talk about calcium overload. I would be really worried that that would cause issues with stones forming from so much given at once.
I've not had any trouble with the cuttlebone and I've been using it on and off for quite a while. It's not an every day thing here because I rarely have a calcium issue though. I wonder if there are different types of cuttlebone. I usually get mine from an online bird supplier and it breaks up easily and doesn't appear to be sharp.
If there was an issue with it being sharp, I would really find it hard to believe that it would be any more sharp than a splintered piece of wood or a broken popsickle stick that I see people give their chins all the time, especially doing so much damage as to cause bleeding to death?
You can also get a calcium powder on line. I just know I use TUMS for heartburn and they are sickening sweet. One bite of a TUMS isn't going to do anything if you need calcium, you're going to have to give it every day for at least a week, and to me that's just too much sugar.