WSO2 API Manager provides resource level authentication where you can specify the authentication mechanism for each HTTP verb. If you set it to 'None', then you do not need to set Authorization headers when you call the API.

As given in the document[1],when creating the API set 'AuthType' value as 'None' for all the HTTP verbs.

[1]http://docs.wso2.org/display/AM150/API+Resources