Assuming all your parameters are posted you just need the following: (note that the posted names must match the method parameter names)
//Put operation
[OperationContract]
[WebInvoke(Method = "PUT", RequestFormat=WebMessageFormat.Json)]
vTranscript UpdateTranscript(string transcriptId, string quizId, string choice, string mbox, string status);
UriTemplate is to define parameters that are embedded in the url itself.