Not sure I follow what you mean by "non-web-access email"
Most email providers give you the settings to interact with their mail service through whichever email client you like over a number of different protocols (POP, SMTP, etc). The majority also allow you to log in via a web client, but it's up to you really. You can use the android mail client to connect to hotmail or android outlook to connect to gmail. Can even add multiple email providers to the same client if you like.