If they are three weeks old sounds like it's time for their waterer to be raised up a bit. Raising the waterers and feeders as they grow helps keep both the waterer and feeder cleaner, but to answer your question it's not going to hurt them to drink water with shavings in it so long as there is enough water that they don't run out.
I have a variety of ages in my juvenile coop right now, with the youngest ones (standards) being five weeks old. My juvenile coop is divided into sections, with the youngest starting out in the smaller brooder section. Last week, in preparation for even more chicks due at the end of this week, the youngest were introduced to the older (bantam) ones who are now 20-ish weeks old. Some chasing, some pecking but everyone is fine. They are all drinking out of a standard 7 gallon waterer and yes, still kicking shavings in it even though it's up on a paver. I plan to raise it even more this coming week by adding another paver.
I learned long ago not to stress over chicks. They all start out on shavings, they all get baby feeders and waterers for a few weeks, then on to the big girl (and boy) stuff. I do
not sanitize everything daily because I want them to be introduced to germs to help build strong immune systems. I don't let them live in filth, but they do need that exposure to germs. At integration time I watch for excessive chasing and pecking from the older chicks and would intervene if it got out of hand (hasn't happened yet). I just enjoy my chicks and worry about problems as they come up, not lay awake at night thinking of all the things that
could go wrong. I have had great success with the enjoy more, worry less approach.