I put my phone number on my cards - if you google most people’s business details you’d get the number from Google anyhow, and personally I don’t buy from anyone if I can’t see a number or, alternatively, a home address. I can think of a couple of Facebook examples where people have stressed their family business background and their personal service, and yet the only way of contact is an Info@ email address (no home address, no name of the person running the business and no telephone number).
I understand the preference for email - that’s mine too - but to be honest, people very rarely call as most other people’s preference is for email too!
If your business is a hobby, and you are uncomfortable about speaking on the telephone, just give your email address. If you want to grow your business to something that supports you financially then I think you do need to put a telephone number (or as I have said at least a home address) both on your website and on your business cards.