You will not be able to - the process requires validation to be performed on the server. You will need to use your own formmail script that is designed to perform the validation.
The reCAPTCHA site has excellent documentation for web developers. And here is an example of modifying an already excellent formmail script to work with reCAPTCHA. You can download the nms-formmail script from http://nms-cgi.sourceforge.net/scripts.shtml
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