Check out this link. http://www.larimarspaaruba.com/ The people from the Spa will come to you to do hair and makeup. However, this is quite a distance from Baby Beach. Good Luck and congrats on your upcoming wedding.
Since your wedding is taking place at Hyatt, I am sure the wedding coordinator there will be happy to make an appointment for you with their hair salon. Their salon has excellent hair stylists and makeup artists and for convenience sake, you are better off going to the Hyatt Salon then having your hair style and makeup done in your room. Plus, it is much easier to get your hair washed in the salon then in the bathroom sink. If your ceremony is scheduled for 5 or 5:30 p.m. since sunset October 18th is 6:19 p.m., my suggestion is to have Hyatt's Wedding Coordinator make your appointment at 1 p.m. In this way, you should be finished by 3 p.m. and will have enough time to get dresssed and not be rushed. Especially if you having the photographer coming to your room for pre-photos. Just email your coordinator ASAP since October 18th is right around the corner and you do want to make sure that 1 p.m. is available at Hyatt. Also, if you have anyone else in the wedding party that needs their hair done, make sure you make their appointments early enough.
I just got married in Aruba in August. I used Georgie and Clyde from Stars Hair and they came to the hotel room. They did a nice job on my hair (I had a trial) and all of my bridesmaids. But I know Tita also has people she can recommend to you. Good luck!