I am going away and will not have access to my cell phone, how am I going to access my email?

wish I had the answer but since I'm the one that asked the question, that would be a NO, don't think I could be much help

Before you go away go back to signing in with a password by disabling your account key you set up to go to your call phone.

Disable Account Key or manage devices 

You can turn off Account Key and switch back to a password, if you prefer. Or, if you're using multiple devices and Yahoo apps, you can change where the notification is sent. 

Disable Account Key from a web browser 

Go to the Yahoo Account security page. https://login.yahoo.com/account/security?.lang=en-...

By "Yahoo Account Key," click Manage. 

Click Disable Account Key at the bottom of the screen to switch back to a password. 

Optionally, click the toggle to the right of any device you want to turn on or off.

go to a library any computer or get a tablet

Verify your account after signing in: https://help.yahoo.com/kb/sln8923.html

Have it forwarded via pigeon

If you are in a hotel, they probably have a wifi network available for you to log into with your computer.  Airports often have wifi networks you can log into.  You can often log in at places such as Starbuck's, or McDonald's.  Public libraries often have limited log in times, but you may have to reserve a time, and you may be prevented from logging onto porn sites.

Ever heard of a library?

you might be able to do that at the library

that's what computers are for.