We did this with Swedish BankID but added it as an integrated formblock. 

If the BankID formblock was present in the form the submit button was disabled until the BID authentication had been performed.

Which external signing service will you use? Is there any API:s?

If you're looking to update form data without resorting to direct database access, you can do this by getting the appropriate instance of IPermanentStorage and calling the UpdateToStorage method. Here's an example though, for simplicity, I've hard-coded the form ID and the submission ID, and I've used ServiceLocator:

//First get the storage provider for the form in question
var storageFactory = ServiceLocator.Current.GetInstance<SubmissionStorageFactory>();
var formId = new FormIdentity(Guid.Parse("b100041d-15a3-49a3-b107-f3443460b5b8"), "en"); // <- shouldn't be hard-coded
var formStorage = storageFactory.GetStorage(formId);
            
//I've hard-coded this but you'll probably want to fetch it dynamically e.g. from the querystring
var submissionId = "6BDE1012-43BC-42DF-ABFA-0195E06612D2";

//Create a submission object with the data fields we want to update
var submission = new Submission { Data = new PropertyBag(), Id = submissionId };
submission.Data["SYSTEMCOLUMN_FinalizedSubmission"] = true;

//Persist our changes
var returnedSubmissionId = formStorage.UpdateToStorage(Guid.Parse(submissionId), formId, submission);