A year's worth of floss picks is the same amount of plastic as just a couple of bottles/containers. If you feel bad about the plastic waste but can't find an alternative, you can always focus on getting fewer single-use plastic containers.
There are also wooden ones; still making trash but at that point it's equivalent to a bad toothpick habit lol
When I looked into them, a lot of people seem to speak highly of Shokz/aftershokz. I haven't used them so can't make a personal recommendation.
One thing to note is that if you want them for swimming you need to get ones with built in storage bc Bluetooth can't really penetrate water