Hey TheAlphaLegend,
We're having a bit of trouble understanding the issue you're facing.
To clarify, you want the 'swish' sound when a new email comes in, but it also vibrates and you do or do not want that to happen? Or what do you mean by "both appear"?
You can see how to set various notification sounds here: Change message notifications on iPhone - Apple Support
"Change the sound and vibration for notifications
You can choose the sound volume for alerts, choose between a tone or sound for alerts, or change the notification vibration pattern (when the phone is silenced).
- Go to Settings
> Sounds & Haptics. - Do any of the following:
- Make notifications quieter or louder: Adjust the volume with the slider.
- Choose a tone or sound: Tap Text Tone, then tap a sound below Alert Tones (or tap Tone Store to download one).
- Choose a vibration pattern: Tap Text Tone, tap Vibration, then choose an option (or tap Create New Vibration to make your own).
- Tip: The tone and vibration you choose apply to both the Messages app and other apps that have notifications on, such as Mail, Phone, and other Apple or third-party apps. To change them just for the Messages app, go to Settings > Notifications > Messages, then tap Sounds.
You can set how many times to repeat a notification (from Never to 10 Times) in Settings > Notifications > Messages > Customize Notifications."
Otherwise let us know more specifics as to what you're trying to do, or what you expect to happen but does not.
Cheers!