Hi
Not a complicate task. I recommend you to use Expect, which is TCL based and run in any linux out there.
You can do this in two ways: Put the script on the Cron so that the Cron can control the days you want to run the script. This is the best way in my opinion.
And you can also create a logic inside the script so that the script will sleep until the day you want to execute.
I´ll share a very simple script that is able to access a device and issue a command. You need to edit the script and add some logic but you get the idea.