thrums

I had a t-shirt printed for my son, but the image is not well-defined. I would like to outline the image, but am not sure what type of pen/marker/pencil to use to make the outline permanent. It is a black t-shirt so I'm looking at a grey or white color. I want it to look like an intentional outline of the image (blend with the print) rather than using a puffy or 3-D medium.

I have seen that Sharpie has an oil-based permanent marker, but have never used one on fabric. Would this work on cotton or are there better products? (eg. a medium that once applied is ironed into the fabric to make it permanent)

Your suggestions are appreciated. Please include suggestions of where to purchase the product. (It's a Christmas present.)

Thank you so much.