There are no restroom facilities on the island. Your boat will have one as the previous poster said -- tho the boatman will drop you off and then for 2 hours while you are on Skellig Michael you are without access to a restroom. The boatman will pull his boat away from the landing area and will wait for you out on the water. You must remember to pack a lunch and water to take along.
Fair warning, it can be VERY rough on the water. The day we went in early June was rough -- the sea swells were HUGE --and we didn't get to land after a long boat ride. 3 of the 10 on board our boat were seasick. Our boat left out of Derrynane harbor and took 1 hr 45 min to arrive at Skellig Michael. -- then we didn't get to get off! I would reccommend taking a boat from PortMagee if possible-- it is only a 45 min boat ride from there. Most boatmen leave from PortMagee -- Des Lavelle, Joe Roddy, Joe Pat Murphy are some of the names. We rode with John OShea out of Derrynane -- nice guy, just a long ride.
I have a seasickness medicine call "Motioneaze" that I got from a local marine supply store near my home -- tho is can also be purchased on line. It is liquid, comes in a small bottle and is applied to the soft area behind the ear. And can be used AFTER you begin to get sick. It does not make you drowsy either like so many others do --like dramamine. This definitely saved the day for the 3 sick ones on our boat!
Skellig Michael is an amazing place. I hope you are planning to go soon before the puffins all leave for the season in early Aug. That is the main reason we wanted to land on the island. We wanted to see the elusive puffin up close. They nest by the 1000's on Skelllig Michael. I hope you have a calm, clear day for your trip. If you do then you will be one of the rare lucky ones!