Some stores allow you to write down the coupon code and use it at the time you make your purchases. However, some stores do require you to have the printed coupon before they will authorize the discount.
If you want to play it safe, I'd do everything possible to print out what you need.
If you do not have a printer, you can go to the public library (it's free except for the cost to print), to a print shop or copy center such as Kinko's, or ask a friend or neighbor if they would be willing to print a few pages for you.
Good luck!