I think its great that you are concerned about your pets' teeth. So many people forget that, just like us, pets need dental attention too!
The first question I have for you is when was the last time that your Chihuahua had her teeth cleaned? If there is significant tartar built up on her teeth, no amount of brushing or water additives will help to remove the tartar. You are correct though, if she has lost teeth due to peridontal disease, her remaining teeth and gums might be sore, so I understand your reluctance and concern.
Once you have a professional teeth cleaning done, your veterinarian can apply a barrier sealant to help stop plaque from building up and actually extend the period of time between dental cleanings. You can help with this at home by "re-applying" the product once a week. It doesn't take a large amount and the natural action of the tongue and saliva help to coat the teeth. The product is called Oravet.
Another option is a product called AquaDent. It is a water additive that helps to fight plaque and freshen breath. You add a small amount to fresh water daily. This product does contain Xylitol, which can be toxic to dogs if they would try and drink the concentrated solution, so be sure its kept out of their reach and follow the label instructions.
I couldn't find any information that said Listerine would be bad to use, but I don't know if that small amount in their water would be very helpful to you.
So...to recap...a professional dental cleaning should be considered. Use a barrier sealant to help slow down plaque progression. If her teeth are in good shape after the cleaning and she will let you do it, consider brushing as it is the best way to help prevent the formation of tartar. And, as mentioned above, consider using a water additive to help.
Hi Jana:
I understand your frustration. Actually accomplishing the home dental care is harder than it sounds. It does take patience and practice and really getting the dog used to you handling their mouth etc.
I seriously doubt that a drop of listerine would do anything. Dosing anything in a dogs water is ineffective because of the immediate dilution, and lack of controlled uptake. That is why this Dr. Franks Pet Pain Spray is such a joke. Anything sprayed in a dog's water become so dilute and no one can predict or guarantee A) dog will dring, B) dog will get an effective does and C) tomorrow that water should be thrown out and replaced with new. About the only place I have seen water dosing do any good is with birds.
That said (you probably know what I'm going to say now....) your veterinarian is the one that should examine, and clean / treat the teeth. They can see all parts of the mouth and teeth / gums.
There is a new barrier sealant gel called OraVet they can apply and then you continue with the weekly treatments at home. Pretty easy to apply.
Believe me I KNOW how not fun it is to try to brush or treat pets teeth at home, but it is important - but only after - proper cleaning and treatment at the vets office.
Finally there are special dental diet foods, some types of chew bones and biscuits that actually help with tartar.
Please try working with your Primary Care Veterinarian as good dental health will save you money and heartache in the future!