Add this parameter to the snippet-call with your own web-groups:
[tt]&deleteGroups=`Registered Users,Site Admins`[/tt]
"The downloadGroups parameter will make the download link active for users that belong to the specified groups. If a user is not logged in they will receive a JavaScript alert with the message contained in the noDownload language setting. Multiple groups can be specified by using a comma delimited list."
Use the [+fd.delete+] placeholder in the file/row part of your template like in the default one:
[tt]<td><a href="[+fd.link+]">[+filenumber+]. [+fd.filename+]</a> <span style="font-size:80%">([+fd.count+] downloads)
[+fd.delete+]</span></td>[/tt]
And use the delete-part in the template after the file/row part like in the default one:
[tt]<a href="[+fd.deletelink+]">Delete</a>[/tt]
And an enabled javascript in the browser for the confirmation-alert.
Nothing more you need, I think...