Follow the provided instructions in the Package Download Assistant for the Skype v22.214.171.124 package, which says:
This link will take you to the Skype for Windows download page. Choose the Skype Free - Download Skype button to save the SkypeSetup.exe file. Once downloaded, choose the Import Source button on the top left of this to upload the binary to the Patch Manager server. Double click the download URL to launch the default browser.
I guess I got put off to a different download when I had to sign up for the service. I just went back through the same steps and got the exe.