No, you don't need to print the payment voucher. Just make the payment using whichever site you prefer from the list (get a receipt from them for your records) and you are all set.
(When you say print and send 1040 form, I am assuming that you e-filed and you mean the 1040 payment voucher - if you are actually printing and mailing your taxes by mail, then you would still need to print the 1040 and mail it but without the check and voucher).
