I've used a few wood burners and unless it's a really nice one that you can crank up the heat on, I'd pass on that project, lol. Also some wood types just don't play nicely with wood burning, such as heavily grained hard woods
What about simply painting the sign?
Why doesn't he make the sign? lol
I'm guessing your "engraver" is a rotary tool with the router base? A rotary tool with the router jig attachment should be sufficient to do this if it's what you're working with. If you have the "plunge" router attachment it should give you more dexterity and...