Personally, I would not destroy a perfectly good genuine brown striped bag by dying it black, which will result in an obviously faked bag with discolored and likely peeled and chipped off silk screened lettering. That's akin to useing household interior latex to brush paint a vintage Cadillac with sunfaded but original lacquer. Examine the weave of the brown bag inside and out and marvel at the multicolored multilayer weaving process to produce that unique texture & pattern.
I would go to the fabric store, select some good thick black fuzzback upholstery moleskin and sew up (or have my Mom, or someone who can, do it for you) a replacement bag for display purposes, as I agree a black bag would look better.
You could even duplicate the bag graphics quite well using fabric paints and a steady hand. At least then it would be a 'genuinely fake' bag until an extremely rare one chances to come along.
Dave