I don't have enough Windows scripting experience to give a definitive answer, but I would suggest that first of all, you use Pageant to manage keys to access the remote *nix servers. Also make sure the PuTTY directory is added to your PATH.

you then use PSCP to copy the script to the remote host:

Code:

pscp -agent \path\to\source\file user@remotehost:/path/to/target

Then you use Plink to make it executable and run the script:

Code:

plink -agent user@remotehost "chmod +x /path/to/script; sh /path/to/script"

You could probably wrap this in a Windows batch script, but I'm not sure how to make that completely robust.