No, you should not drip water in her beak.
Either give her a dish of water, or leave her without.
If you give her a dish of water, you could put in some marbles or clean rocks, so she can dip her beak in between them to drink but cannot get herself all wet. (Many chicks do fine with a plain dish of water. But sometimes the rocks or marbles help, and sometimes they keep the person from worrying.)
Dripping water in the beak is more dangerous than letting the chick drink on its own, so do not do it unless you have a case where the bird is unable to drink. (You really do not want water in the chick's lungs, and the chick is better than you at getting the water in the right place.)
It is fine to offer water even if there is no food.
When do you expect the chick starter to get there?