"Cloning" a HttpResponseMessage to a HttpResponse

Question

For a project I need to build a "proxy" for an third party API because parts of the API should be blocked for an external party. Now I can use HttpClient to retrieve the information from the API but I need to send the information back using HttpResponse. For a lot I can send information back but sometimes the information is send back as gzip or binary. What I'm trying to do is copying all Headers from HttpResponseMessage to HttpResponse but I fail miserably. Does anyone done something like this?

    public static void AddHeaders(HttpResponse httpResponse, System.Net.Http.HttpResponseMessage httpResponseMessage)
    {
        httpResponse.CacheControl = httpResponseMessage.Headers.CacheControl.ToString();

        foreach (KeyValuePair<string, System.Collections.Generic.IEnumerable<string>> item in httpResponseMessage.Headers)
        {
            AddHeaders(httpResponse, item);
        }

        foreach (KeyValuePair<string, System.Collections.Generic.IEnumerable<string>> item in httpResponseMessage.Content.Headers)
        {
            AddHeaders(httpResponse, item);
        }
    }

    public static void AddHeaders(HttpResponse httpResponse, KeyValuePair<string, System.Collections.Generic.IEnumerable<string>> keyValuePair)
    {
        string key = keyValuePair.Key;
        string values = "";
        foreach (string stringValue in keyValuePair.Value)
        {
            values += "," + stringValue;
            values = values.Trim(',');
        }
        switch (key)
        {
            case "Content-Type":
                httpResponse.ContentType = values;
                break;
            default:
                httpResponse.Headers.Add(key, values);
                break;
        }
    }