I believe you can get a "fresh" URL that will launch the envelope documents (in view-only mode, assuming the recipient has previously completed signing) by simply issuing another "POST Recipient View" REST API call for that recipient. DocuSign will know that the recipient has already completed signing, so the Envelope will open in read-only mode when you launch the URL returned in the POST Recipient View response.
Keep in mind that each URL retrieved with the "POST Recipient View" request only works for a certain amount of time (5 minutes?) after you retrieve it -- so you'll want to not make the API call to get the URL until the time at which the signer has indicated that they want to view their envelope...then once received in the POST Recipient View response, immediately use that URL to launch the envelope.