Hey there @salif.de - great question!
At this time, the “add times to email” feature will not translate to messaging on other apps/platforms. When sharing via Whatsapp/Messenger, you’d have to share your regular booking link.
That said - there’s a solution that might be perfect for you, yet! Our Customize Once and Share tool allows you to share an existing event type, but in a customized way for a single invitee (with a single-use link). This means you could change your availability for the person you are sending it to (using date specific hours, or, by removing specific days/times of the week and leaving what you want them to select from) before then sharing that link with them via Whatsapp/Messenger.
I hope this helps!