How to replace json `key` recursively in javascript

json_key_replacement.js

// change key as per requirement - I have used ":" in example JSON object below
var replace_key = ":" 
, add_key = ""
, rwp = function rewriteProperties(obj) {
    if (typeof obj !== "object") return obj
    for (var prop in obj) {
        if (obj.hasOwnProperty(prop)) {
            obj[prop.replace(replace_key, add_key)] = rewriteProperties(obj[prop])
            if (prop.indexOf(replace_key) > -1) {
                delete obj[prop]
            }
        }
    }
    return obj;
  }
, org = {"organization":{":employees":{":male":{":profile":{":first_name":"Jason",":last_name":"Brad",":age":40,":email":"[email protected]",":address":{":street_number":5,":street_name":"company avenue",":post_code":"12345",":city":"Big city",":country":"United"}}},":female":{":profile":{":first_name":"Jane",":last_name":"O'Coner",":age":35,":email":"[email protected]",":address":{":street_number":9,":street_name":"office street",":post_code":"56789",":city":"New city",":country":"New Country"}}}}}}
, newOrganization = rwp(org)

console.log(newOrganization)

// OUTPUT: newOrganization object will have no ":"