Enter "International Telegram." This service supposedly inherited Western Union's telegraph system. This is part of the explanation from their website: https://itelegram.com/
They're not cheap, but "novel and fun" usually isn't. LOLWestern Union sent its last telegram in 2006 and the telegram service was turned over to International Telegram. For over 18 years, we've kept up the same great service you know and trust. We're the only real telegram company!
Now, if only I could pay extra to have a 12-year-old boy in a courier's uniform deliver the message on a bicycle...