To hide the parameters you would have to do a POST request.
There are two problems with that:
The CF script would have to support POST.
You can't do a POST redirect with any reliability. There are some browsers for which it works, but for most it doesn't.
If you absolutely need to do this, you should use LWP::UserAgent, make a POST request, and then print it's result. The only drawback is that your CF script will see all the requests coming from the server running your script - that may or may not be a problem, depending on your application.