Is there a way to share your screen without any possibility of being recorded? Every screensharing utility I know, Skype, Join.me, Teamviewer, RingCentral, are all recordable via screen recording app. Is there any way to prevent the person from recording?
No, because you can't control the endpoints that are connecting to your screen sharing session. Basically, even if the software you are using doesn't support them recording your session, there are other third party apps available that will do so. Privacy isn't a given once someone has access. They could record it with a phone or another device as well.