[MsNobleEleanor]

When you add your phone number to the account you have the option to delete the phone number in the app. Currently, I have my phone number for two accounts for Twitter and it works fine. Twitter will ask if you would like to sync your contacts in your phone to twitter, you can deny this, your contacts will not know about it.

If you go in the app once you add your phone number go to 'Settings and Privacy' -> 'Account' -> 'Phone' -> option "delete phone number"

You may need to add an email in the email field if it's blank. That could be the reason why they want you to confirm and use your phone number. You can create an email with something similar to your twitter name or something if you haven't done so already.

I hope this helps. Let me know if this works, if it doesn't I'll see what else might help.