Вы можете использовать System.Net WebProxy, как показано ниже.
var request = new RestRequest(funcName, funcType);
request.RequestFormat = DataFormat.Json;
request.OnBeforeDeserialization = resp => { resp.ContentType = "application/json";};
request.AddBody(param);
RestClient restClient = new RestClient(url);
restClient.Proxy = new WebProxy(myProxyUrl, myProxyHost);
restClient.Proxy.Credentials = System.Net.CredentialCache.DefaultCredentials;
var value = restClient.Execute(request);