Hello @David1936,
The host will already have the phone number that you registered with Airbnb. It's visible to them once the reservation is confirmed.
The will also have a temporary email address, not your actual one, which they can use to email you.
You can point out the above to them. The number and temporary address will be visible to them if they click on your reservation in their reservation list.
Don't give them your real email address as, as you point out, communications will be out the Airbnb system if they use it.
Steve.