Having been a Music Educator & Church Musician for many years, and also working as an activities/social services director at nursing homes/Sr. residences, it is quite normal for me, also, to play for nursing homes-which led to playing for the dying. One of the most important things I learned is to respect the needs of the person re their Music preferences & Religious preferences. It's all about their needs, not yours. As an Activities/Soc Services Director, if I ever heard any visitors "witnessing" to a very ill/dying resident, I would take the visitor aside, & sometimes have tossed them out--screaming to a resident/patient about burning in hell is never appropriate. I'm happy to play or sing whatever they want to hear, as long as I know it. I'll play Classical or Celtic (or whatever), and I'll sing most anything from Western Swing to Ave Maria in Latin. [Only if asked to, I'll pray with them any prayers, Protestant, Catholic, Jewish or other.   If asked, I'll read to them from any scripture printed in English.]
I never presume that people want to hear hymns or any other specific Music. I never presume that a person wants to chat, or have a chatty person around them. Some people are not verbally responsive, but one can learn to be quite observant of others. Sometimes you can speak to the family members to ask about Music preferences, but sometimes no family is available. When in doubt, instrumental is a good place to start.
If you have the opportunity to be a regular volunteer at a specific nursing home, you can get to know the bed patients quite well by playing for them on a regular basis. You can often find out about their preferences from staff members as well as from playing for them over time. When their time is short, the staff often knows & can tell you, and this is the best case scenario for being able to provide comfort with appropriate Music.
It really helps if you are willing to learn some of the songs of their eras. Many people, however, will prefer only soft instrumental.    My preferred instruments to play for the ill & dying are Harp, Autoharp, & Mountain Dulcimer or Guitar fingerstyle.   If you play Mountain Dulcimer, try fingerpicking for a harp-like tone.
Remember our Veterans Hospitals & homes, too.