I’m not sure why you’d do this unless you also wish to remove the labels underneath the fields. This leaves it to your visitors to fully delete or highlight and replace the ‘Name (required)’ and ‘Email (required)’ before sending. Keep in mind, you would loose any changes made to this plugin when updating.
You should try Contact Form 7. This plugin allows you to easily create customized forms for use throughout your website. You can specify any fields you wish to include, their default values, labels, format the email(s) you will receive, and edit the messages returned to the visitor. You can also add an optional CAPTCHA to avoid spam (Requires: Really Simple CAPTCHA). Each form generates a shortcode that you can place in a page, post or text widget in your sidebar. It also uses AJAX and does not require a page reload when the message is sent.
It may not seem as easy as simply adding the shortcode provided with ‘Send E-mail’, but I think you’ll find the form editor easy to use and very flexible. Just ask if you need help creating a form.