Those steps won't help without a phone number to actually give my account. I have to add that before I can do anything else. Thanks for your suggestions though.
Since it's money and you're worried to let someone know your credentials/access your account, only way is to follow support's advice. Don't you have a family member with you that has a mobile, or a friend?
It has been an issue to me as well before. Such a hassle that I need to install the app first and open it everytime I log in my account on a web browser. They seem to not consider the idea of a user not having a phone.

I am not sure how you take the region as the issue on accessing the xapo wallet. I was using the xapo wallet for some months before but I did not find the issue on accessing the wallet at all.
Since i am from the Asian region and I did not find the issue on accessing the wallet at all mate.
You may login to the wallet and write a support ticket for the assistance from them with the below link.
https://tpi.xapo.com/contact-us/?lang=en