Soda is not nice stuff to get in your eyes. Not even slightly.
As someone who has worked with dangerous chemicals I would advise you in the strongest possible terms to never ever go at a lump of soda with a hammer in such a way that it might produce splinters.
Don't do it.
If you really must break it up, then it is a use for old shopping bags. Put soda in the bag (preferably double bagged), and hit it, preferably with a lump of wood.
Soda sucks water from the air, indeed it will suck it from your skin given a chance. Sealing will work for a while.
Soda is a useful cleaning chemical, used it nyself.
It is not a "natural" cleaner and it requires quite a bit of energy to produce, but probably no more than modern powders.
I do find the link more than slightly misleading.
Soda is not biodegradable, in the sense that anyone I know uses it.
If soda comes into contact with almost any form of life, it will start to dissolve it. That is why it is an effective cleaner, most stains are biological, and it attacks almost all biological material, living or not. If there is enough of the organism, then it will be used up.
By that logic, hydrochloric acid, hydrogen cyanide and napalm are all biodegradable.
Soda does have the advantage that you're really unlikely to have an allergic reaction to it, though it will dry out your skin far worse than anything you are likely to have in your house.
Put a few tablespoone of hot water into it.
It's happened to me expat, the water will sort it out. Put it in one of your containers and add water.
Later, when you come back to it, it will have softned it up. Don't waste your energy banging it