In boarding schools if you interview over Skype does it hurt your chances in any way? Specially, Exeter and Andover!
No
Unless things have changed in the past few years, both Andover and Exeter offer alumni interviews. I’m sure someone will correct me if I’m wrong, but I don’t think either do Skype interviews as a matter of course. One other option, if applicable, is trying to pick up a interview slot if an AO is visiting your area, e.g., for a TSAO information session.
It shouldn’t be a major obstacle. Of course, if you can visit campus and meet with an AO then that is preferable, but Skype works as well. My son did many in person interviews and one Skype and will be attending the one where he did Skype.
Most of my kid’s interviews were over Skype. It did not affect admissions results. Pro-tip: You can stick a Post-it with key talking points right next to the computer’s camera 
Our DS did a few interviews over Skype and others on-site and we did not see any difference in his acceptance. However he did to an online interview with Loomis using their tool and wow did he struggle with that interview as he was only answering pre-recorded questions. To our surprise Loomis was the only school he was rejected at.
Our kiddo did one interview via Skype and another was actually via FaceTime - we got creative - both were very positive and actually worked out well! I think Kiddo was more relaxed and came across better via Skype or FaceTime. Generational thing maybe?