You can use dry transfer lettering like Chartpak, or Letraset. Basically it is sheets of lettering (the full alphabet with multiples of common letters, plus numbers and symbols) that you can apply via rubbing the plastic sheet on one side, depositing the letter on the surface below the other. They come in a many fonts so you should be able to find one that matches.
Transfer lettering was pretty common before the digital age and is still used in places like art galleries to put titles on the walls next to an art work. It is an easy way to get professional custom lettering on objects, though it takes some practice to keep things lined up.
Alternately, for a much more complex but professional solution, you could make a screen print of the whole design. Probably over the top in terms of expense but then you could match the type exactly. Process would be to capture the design to computer, clean up and reproduce with digital tools like illustrator or photoshop, print on masking, then use that to generate the screen. Unless you have experience with doing this you would probably want to farm this out to a screen printer familiar with printing on objects other than tee shirts or paper, at least the last part of the process.