Tattoo Image Recognition - Should I Crop Training Data Background
It is really hard to give an answer on what would work best, as Deep Learning is often based on experimenting with different things. But I would highly recommend you start quick and dirty. This is an advice given at all universities or by the famous Andrew Ng. Just start with the easiest model and then iterate. For example if your simple model doesn't work try to create a more complex pipeline by preprocessing the images as you suggested.

In Deep Learning, time is most often the biggest factor. Don't waste it by trying to create a highly complex model to then just observe that it didn't help to improve your model.

I would like to add, if you decide to add more parts to your pipeline, for example 1) Find the human in the image 2) Find the tattoo 3) Classify tattoo etc. you should take a look at this video as it explains how to improve your pipeline in the most efficient way.