There is a better workaround! I found this StackOverflow thread:
http://stackoverflow.com/questions/3980064/create-wufoo-webhook-with-p ut-request-in-coldfusion
ColdFusion will still send the request body with PUT and DELETE requests, so we can format the request body as a form field (or series of form fields).
<cfhttp url="#uri#" result="result" method="delete">
<cfhttpparam type="header" name="Content-Type" value="application/x-www-form-urlencoded; charset=UTF-8" />
<cfhttpparam type="body" value="FormFieldKey=#UrlEncode(FormFieldValue)#" />
</cfhttp>