That's definitely a cool idea! I might ask around different webshops to see if they're interested in something like this.
One way this can be accomplished is by removing all shoes with such logos from the training data. But Nike and Adidas are disproportionally large parts of my training set, so this would not be feasible.
The other option would be to train a machine learning model to recognize said logo's and to use this model to remove sneakers with logo's from my generated images. This could however greatly reduce the variety of images on the website.