Convert sketch to vector for T-Shirt

Customer provided hand drawn sketch. Need it in Illustrator (vector) format for use on a T-shirt. Size should be adjustable after completion. The shirts will be teal in color. The art work should be done in black only, does not need to show any color, as I will be using a vinyl cutter, which cuts along the black lines of the artwork. Final artwork does not have to match exactly, but should 'resemble' sketch.