You can use your alternate email to get the verification code, if the Account Key can't be sent to your mobile phone.
On the sign in page, enter your Yahoo email address and click on Use text or email. You will be invited to use your phone number or alternate email.
Then follow the instructions to get the verification code to your alternate email. Once you have recovered access to your account, you will be able to update your phone number or disable the Account Key, from your account security settings.