Well, we all know what you mean! It's true the inversion is not needed in your case; nevertheless it's a neat way to make a "transmap" from the original image. Here's something to go with it, for use with coloured tattoos.

If your tattoo is lighter than black or a multi-coloured image, it may not have high enough contrast to produce a strong blend, and the underlying colour will tend to wash out the tattoo colours somewhat. The top Blender node in the image shows this. (I've just used a simple colour for the underlying skin colour).

But if you plug in a Bias node with a very low Bias value, it will create a high-contrast version of the original image, in which everything but the white background is converted to nearly black. The Blender_2 node shows the high-contrast version, and you can see the tattoo colours are blended at near enough full strength.

You can invert the Bias node to produce a "transmap" if you needed it.

"If I were a shadow, I know I wouldn't like to be half of what I should be."
Mr Otsuka, the old black tomcat in Kafka on the Shore (Haruki Murakami)