Coconut is not really a nut, though the FDA now classifies it as a "tree nut". It is not cross-reactive with nut allergies in general; see for example this page discussing nut allergies.
Coconut is not a botanical nut; it is classified as a fruit, even though the Food and Drug Administration recognizes coconut as a tree nut. While allergic reactions to coconut have been documented, most people who are allergic to tree nuts can safely eat coconut. If you are allergic to tree nuts, talk to your allergist before adding coconut to your diet.
As such, allergy concern should be similar to that of other foods; serve it on a three to five day period where no other new foods are served in order to identify if an allergy exists (well, in order to know what the allergy is from if it's served).
Fresh coconuts are not highly dangerous from a food safety perspective, but like almost all raw foods can have some risk of contamination with E.Coli or Salmonella. This Cooking.SE question discusses this to some extent.
As such, at minimum wash your coconut carefully before handling or opening it (even though you're not eating the outside - washing is to remove any pathogens that might get on the knife blade or hammer or whatnot while opening, and then pass to the inside). Safer would be to boil the water before serving, though I don't know what changes that might induce on the coconut milk itself. Ten months old is old enough to be somewhat safer from foodborne illness (than a 3 month old), but is certainly young enough that you should be very careful.
Cooked coconut products, subject to the normal care you take in cooking, storing, and serving food, should be perfectly fine for your baby, as long as you take the normal steps documented above to verify he's not allergic.
This page of baby food recipes goes into some more detail than I do above about these topics, plus discusses the different ways you should prepare the different parts of the coconut.
Finally - you should pay attention to choking hazards as well when giving your baby coconut meat or shredded coconut. Either give him a small enough piece that it is not a choking hazard (i.e., shredded finely), or take other precautions. Also be cognizant of how dry the coconut is, if it is shredded; make sure he's periodically drinking, or it may be too dry for him and could cause a choking hazard even if it is finely shredded.