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I think that Putty will only display the output in its own terminal window. One solution is the sort of thing that Clay Helberg suggested. Another is to run the perl and shell scripts on Windows. You can do this if you install Cygwin. Then the script output is available in exactly the same way as if you ran any other Windows command line tool.
Even if you still want to run the scripts on the Unix server, you can call them locally with Cygwin's ssh command, something like this:
ssh username@hostname "scriptname arguments"
The output from the local ssh command is the output from the remote script.