Why is it more likely you'll have internet access when you don't have a phone? If you happen to find a computer, what's insufficient about writing an email?
My wife doesn't check email frequently, so SMS (or even better, WhatsApp) would be more reliable.
Maybe an alternative is to store the WhatsApp contact information of people who could help behind a password.
Then, if I need help, I can ask to borrow someone's phone on the street. If they don't have WhatsApp, I can just make a regular phone call instead.
How will you log into your email from a strange computer without your phone. Gmail has required 2-factor auth for a long time.