I agree putting them on a thread is a good idea. I used a salt slurry to clean my Natural pearls at Zeide's instruction. It worked well. I think you'll need them on a cotton thread or even Beadalon thin wire to get those holes clean..... Be sure to rinse them very well, pat them dry and keep them in a dish or shell in a moist room for awhile- like the bathroom or kitchen.
People also use a mild Castile or coconut oil soap, ie dr bronner's, and there is even a liquid you can buy- the "Pearl Doctor" which I have not used because they don't say what's in it, LOL. It works well though. Pearls like water, and they like slightly alkaline, so soap and mild detergents are fine. I also use shampoo if I wear natural pearls into the shower. Please note I only do this for solid nacre pearls- I can't speak for akoyas, for instance.
I would make that into a bracelet as fast as I could, and WEAR it!!!