1. Remove the shortcut from C:\ProgramData\Microsoft\Windows\Start Menu\Programs\Accessories
2. Wait for Start Menu index to update itself.

You can find this folder from the start menu:

1. Remove the shortcut from %programdata%\Microsoft\Windows\Start Menu\Programs\Accessories (You can find this folder from the Start Menu. See image at end.)
2. Wait for the Start Menu index to update itself.

update: There are also two convenient keyboard shortcuts to start Snip & Sketch:

1. Print Screen (Must first enable from "Ease of Access Keyboard Settings")
2. Win + Shift + S (Enabled by default)

The Print Screen shortcut is very convenient. I still suggest removing "Snipping Tool" so "Snip & Sketch" becomes the best match in the Start Menu and automatically shows options like "New snip in 10 seconds."

How to find the directory containing the Start Menu shortcut file to delete: