Almost any word that ends with -een can be assumed to
be Irish

This is throwing down the gauntlet, Bill.

-teen numbers immediately spring to mind, though there the derivation is (fairly obviously) from OE for ten.
I'm sure more "exceptions" will be forthcoming...

the English word smither, a word with no known origin which means just the same as smithereen.
Never heard this one, though maybe that's not surprising if it's an old term. But I wonder aloud if "smithers" were odd little bits of metal left around by the work of a smith ? Does anyone know if odd little bits of metal would be left around by a smith?

That would appear to fit the meaning very well.