I suggest contacting Dwayne's. Their website has their phone number and email address. From past experience, it's not the mailer that's important, it's what's on the cartridge. You should have no problem. What I don't know is if you can send it directly or need to send it through another address.
Little known fact:
Most people don't know that Kodak could have sold prepaid Kodachrome in the US for the last 15 years they sold it. In 1994, due to changes in Kodak's market share and amount of competition, the 1954 decree prohibiting Kodak from selling prepaid processing in the US and the 1921 decree prohibiting Kodak from selling Kodak film under private labels in the US, were both terminated.