Need Help With Email? Ask Your Email Questions Online
This may not be what you want to hear, but without the phone number or backup email on your account you'll have to go through the below steps.
You will have to go to this site https://io.help.yahoo.com/contact/index?page=contact&y=PROD_ACCT&locale=en_USPassword ***** sign in --> Forgot my password *****> Email (towards bottom)Fill out the information to create a ticket with Yahoo.
Checking in to see if you still need help with this issue, if so please reply at your convenience.
It will work if you submit a case with the above link, I'll forward the request on however.