So I'm thinking about dyeing some wood black to use for bandings. I'm curious to know how deep the dye will penetrate into the wood. Can I dye a somewhat larger piece than I will be using and then cut strips from it, or do I need to pretty much get each strip to a finished dimension before dyeing?

Also, once the banding is made, if I cross cut or miter it, will there be a risk of the original wood showing, or will the dye penetrate deep enough for that? What about planing/scraping a few shavings of of the piece?

Any information will be helpful. Thank you.