Is there a way to schedule a WhatsApp message to send later automatically?

WhatsApp itself has no built-in scheduler for personal accounts. Options: on Android, a scheduler app that uses accessibility to send at a set time (clunky), or WhatsApp Business (free) which has more message tools. iPhone has no native way beyond a Shortcuts automation that only reminds you to hit send.

On Android the SKEDit-style apps work but need accessibility permission to tap send for you, so weigh that privacy trade-off. For the odd birthday message I just set a reminder and send manually, honestly less hassle.

WhatsApp Business is the only first-party-ish answer. If you send scheduled messages regularly it is worth setting up, and it runs alongside your normal account.

iPhone: a Shortcuts personal automation can open the chat with the text prefilled at a set time, but you still tap send. Apple will not let it send fully automatically.