As long as the "e-sign process" includes providing the information the bank is required to provide to the consumer about how the electronic delivery will take place, whether (and at what cost) paper copies will be available, the hardware and software requirements, etc., and the consumer consents in a matter that demonstrates his/her ability to access an electronic records in the prescribed manner, you should be fine. One you have the demonstrable consent, you can stop sending the paper statement.
John S. Burnett
Fighting for Compliance since 1976
Bankers' Threads User #8