In Applescript, how do I launch Safari "Silently" open url then close the unseen Safari window
You won't be able to do it in AppleScript : Safari only does something on open windows. 

You should definitely look at Command line scripts like curl. 

The AppleScript to call a shell command takes the form:

set variableName to do shell script "command"


So using your AlertURLString you'd want something like:

set curlOutput to do shell script "curl '" &amp; AlertURLString &amp; "'"


See the curl man page for more details on how to use curl to do things like POST and PUT calls or attach payloads to the calls and what not. It is incredibly powerful.