You don't want to use oil of oregano every day indefinitely, but short term it certainly does no harm to your gums. Some people use tea tree oil which I personally think is way too harsh.
You can't get much better than pure wild oregano oil. Start with just a couple drops and increase it from there. I usually take as many drops as I can tolerate at first. After some minutes the burning sensation decreases as more saliva is produced that dilutes it.