Sea salt dissolved in water would be a better choice.
No foam, no scent, neutral to the native mouth flora.
Our mouth contains native good bacteria. They can protect us from caries, and from any other bad bacteria, and from gum diseases.
If you use a toothpaste, it may kill native bacteria and allow bad bacteria to colonize your mouth.
If you use salt water, it will allow for native bacteria to re-colonize your mouth.
Swimming pool is really not a good idea, if you want to stay healthy.
Swimming in natural ocean or lake is safer, if there are no aligators, crocks or sharks like me around, ha ha, jummy.