For the equivalent of a "paste" operation I would run a command-line utility like ClipOut or paste, redirect output to a file and read the file contents.
return = WshShell.Run("cmd /c clipout.exe > output.txt", 0, true)
Set fso = CreateObject("Scripting.FileSystemObject")
Set file = fso.OpenTextFile("output.txt", 1)
text = file.ReadAll
file.Close
You can get ClipOut here: http://jasonfaulkner.com/ClipOut.aspx
You can get paste here: https://www.c3scripts.com/tutorials/msdos/paste.html
For the equivalent of a "copy" operation I would use the clip command line utility that actually comes with Windows and similar code as above.
About the clip utility: https://blogs.msdn.microsoft.com/oldnewthing/20091110-00/?p=16093