The Open With extension is not the Edit with Notepad++ extension. The later is NppShell.
Open a cmd prompt and enter:
reg delete "HKCU\Software\Classes\Applications\notepad++.exe"
Press Return key and if no error, then it will prompt to delete the key and reply with yes.
Open With creates this key and some others. Removing this key removes the orphaned Open With entry of Notepad++.
Some installers add this key, the Notepad++ installer currently does not add this key so it does not remove it on uninstall.
The duplicate entry is something else. Try:
reg query "HKCU\Software\Microsoft\Windows\CurrentVersion\Explorer\FileExts\.ini" /s
and will print information about the entries to discover more details about the entries. You may see something like Applications\other.exe and if another ophaned entry, can use a similar command to remove it:
reg delete "HKCU\Software\Classes\Applications\other.exe"
Always use care with the registry. Ensure the commands are correct before executing them.
