Absolutely play something you are totally comfortable with, particularly if you are new to performing or nervous.
You don’t say what kind of harp or strings, but breakage would not be my first concern. I’ve never had a nylon break unexpectedly. Wires are also rare (though dramatic if it happens). Even guts usually show signs beforehand (suddenly one string is rather more flat than its neighbors, or fraying shows at the bridge or tuning pin). If any are suspect, Sylvia is right, change them. You really can’t do it in a funeral; you’d just have to play around it. But unless you are regularly having broken strings already, there is no reason to suddenly expect them in the performance.
Arrive plenty early–I plan on a full hour in the room, plus whatever time it takes you to tune _before_ people start arriving. That can be two hours before a funeral “starts” especially since music often starts earlier than the announced time.
Unlike Balfour, I have never been successful in memorizing reliably. When I play for a structured unfamiliar event (like a funeral or worship service) where there are many things going on, _everything_ goes in a three-ring binder, service plans, everyone else’s music, my music, in order of appearance, with copious notes of who does what and when. I always methodically walk through the event in my head. That may not be necessary if you are only doing one piece at a particular time.
One last thing: when you arrive, or soon after, go over the order with whoever is in charge. I can’t tell you how often a family has changed something major, but no one thought to tell the harpist that your piece is now in a different place. That will save a lot of embarrassing moments.
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