I use a form to email script in my cgi bin which works well. You can build your forms as normal and send them to the script instead of specifying FP to handle them.
Make sure it is well locked down and only accepts input from your domain and only sends email to your specified own email. Good, up to date scripts will do this. Godaddy might already provide one for you.
It seems Expression Web, even though it is a new release from Microsoft, still requires FrontPage extensions.
If you are using the previous method of developing forms, then yes, the FP Extensions will be required but only if you rely on FP's validation routines.
With Expression Web, it is designed more for the .NET environment and you work with Controls as opposed to form elements. Your entire page is wrapped in a <form> element when using .NET Controls.
Is there a good workaround to make your forms work on Expression Web?
There is. Don't rely on the FP validation routines. You can easily bypass them by taking the validation off page and placing in an external js file, this will eliminate the need for the FP Extensions. But then you have to consider the confirmation page(s), if any. It does require a bit of work to get it in place, but once it is there, you'll be able to easily manage your forms moving forward.