The sound BlueMail plays when a message goes out is yours to set, and it is set per account, so a work account can send silently while a personal one keeps the chime.
- Go to Settings | Accounts | [select the account] | Compose Sound.
- Turn Outgoing Sound on or off.
Choosing a Different Sound
With Outgoing Sound switched on, a Custom Outgoing Sounds row appears just below it on Android, opening your device's own sound picker. Choose anything your phone offers, and picking the default again clears the custom choice.