I guess you mean to one of the recipients rather than your own email details.
Double opt in is required for the new address. There certainly used to be an option for the webmaster to do this but this only put the new address to pending.
One of the problems with the mailing list is that the anti spam features mean that you can't deal with a direct request to change and address without going through the whole opt in routine. I dropped the service for this reason.
Send your user an email saying what will happen so that they don't get confused. If you can't find the maintenance options just use the links on your site to delete the old address and insert the new.
