what is your PI version?
If it is >7.11, you can definitely use SOAP adapter on sender side to trigger the proxy messages from TM to SAP PI.
Refer to below blog for configuration.
And you don't need to share the wsdl with any team, as the sender would be TM system which will post the messages to PI using the RFC destination.
Coming back to your receiver, your third party should provide you with the web services if you want to send this data from PI to them,
If you don't have such option, you can send this information as a file to them. In that case, you can use File/FTP/SFTP adapter.