Complex drawing and illustrations can also be made into rubber stamps; these may not contain many lines and look more like photographs. It is best to send a few different options of these to your stamp manufacturer; one option would be to increase the brightness of the image then convert the bitmap to a simple black and white image. Here it is best to select a rubber stamp manufacturer that is familiar with these types of images, see below recommendations.
Do give your cartoon character a challenge. Sonny goes cuckoo for Coco Puffs. The Trix Rabbit never gets to eat Trix. The Giecko cavemen never get the respect they want. What these challenges do is make the character more endearing. People empathize with them, and that forms a bond. How important is having an emotional bond with your customers?
If the graphic is a vector image, it will be a snap to edit. Open the clipart image in your graphics editing program, select the area you don't want, and hit delete. It's that simple. However, bitmap images pose more of a challenge. You'll have to use the eraser tool and manually delete parts of the image. Or if you want to delete a section of solid color, you can use the magnetic lasso tool and press delete.