In lieu of dye, consider inks. They'll spread like liquid (because they are) and will penetrate the fabric very well. Once dry, they're fairly stable, and can be set to make them more stable and less likely to stain you or other clothing, spread, transfer to others, and so on.
Google has a wealth of tutorials on various inks you can purchase, as well as ways to "make your own" using combinations of dye and isopropyl alcohol; I would recommend getting two base shirts and using one to experiment with multiple processes from multiple different tutorials. Be sure to test how well it spreads, how "realistic" it looks, how difficult it is to transfer to other materials (fabric, skin, hard surfaces, etc), and how well it holds up to being washed.
Making sure the process you choose is stable is extremely important; historically in cosplay events, there have been major issues caused by individuals using materials (body paints, fake blood, spray-in hair color, etc) that was not stable, and caused damage to the event facility (as well as other people's clothing and costumes) as a result. Many events now have rules about what you are and are not allowed to use, and if you use something that transfers to, for example, a chair you're sitting in or another person's clothing, you may be asked to remove the costume or even leave.