If you want something that is safe, there is an option that we haven't discussed yet.
TheraBreath has been extensively studied by dentists and doctors and is approved by both. It is marketed to eliminate bad breath but it also improves oral health. It has sodium chlorite in it, but I believe the concentration is lower than some of the others. It has been around for something like 20 years now and has proven to do no damage and it gets excellent results.
The nice thing about TheraBreath is that it is available at your local drug store.
When CDS is done properly it should not be acidic. Check yours and see what its pH is. A pH of 7 is neutral.
As far as using an acid in your mouth, just be sure to rinse within a few minutes after using it. Water will do a good job. A little baking soda in the water would be better.
Keep in mind that oxidizers work by having a concentration of them in contact with what you are trying to oxidize for a period of time long enough to oxidize. This means that if you use a high concentration solution, damage to your teeth can happen faster than if you use a lower concentration. However, if given enough time, even a low concentration oxidizer can damage.