Yup antiseptics are good in the case of an abscess if the tea tree oil is too strong for you then use savlon spray instead as its made for sensitive skin and you're treating an infection not a bump so its a bit different than treating the more common hypertrophic scarring bumps which are caused by irritation

I understand you not wanting to use things that are going to affect your healing but its important to clear this minor infection up so the bump stays away and everything goes back to normal. A week of using antiseptic shouldn't really affect your healing time but a abscess that keeps reforming is more likely to lead to a worse infection and added complications!