We all have order forms, contact forms, order buttons, and order processes. This could strengthen the idea that showing a telephone number and an email address could be obsolete. But the opposite is true. There are a lot of people outside who are looking exactly for this kind of information / data just to make sure if this is a real person or a trustworthy company.
Learning: If you fear tons of messages or phone calls – give it a try first. In most cases website hosts and business owners are quite happy if somebody sends a direct message or starts a phone call.