I think it's better to configure a Delivery Profile for every departament.
If you do in the way you are saying, you need to select the Sender Profile at sending time after coded something (I don't know if it's possible to do in this way you want) to get the Sender and set the phone number in your email footer.
Since you already have to select the Sender Profile, you could also select the Delivery Profile with the correct Phone Number in send set up.
Go to Classic Content in Email Studio -> Content
Create a Content (could be free form) with your desired footer, with the phone number (for every phone number, or sender in this case, you need to create one footer)
Then go to Email Studio -> Admin -> Send Management -> Delivery Profiles. Create a new one for every footer, and select the footers you have created before.
And when you are setting up sends you can select the Delivery Profile.