Fresh coconut should be wrapped well or placed in an airtight container and strored in the freezer.
it is not the same as in the cans. Canned coconut has preservitives and sugar added.
I believe you can use a knife and chop fine or use a grater to shred coconut.
although frozen coconut is not available in my area of the united states, some southern states sell coconut in the freezer section, and my cooking friends from the south say it is much better.
hope this helps. Happy baking!