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In this situation, it's best to choose an external e-mail program, such as Thunderbird (free), Outlook (subscription) or App Mail on a mobile device, so there's no need to connect to Webmail with the 2FA.
Don't forget to create a pwd for the external mailbox and to use the IMAP protocol when creating the Bluewin account on the device used.
Set up Bluewin e-mail and fix problems
Find out how to set up Bluewin e-mail on your device (e.g. in Outlook) and solve problems if your e-mail programme stops working.
Set up a Bluewin e-mail account and resolve problems | Swisscom