Hello and thanks for the query
The alternative for the surgery is to go for Ksarsutra Therapy (in ayurveda) but it is a long procedure and chances of reoccurrence is more. It is also like a surgery but procedure is done by a medicated thread.
It doesn't resolve by its own and its better to get it treated as early as possible if it is discharging pus.
Now about your another query about general anesthesia
their a always a risk factor for every procedure in every one. Its just like crossing a road, if bus hits you its your bad luck. Every doctor do their best to treat the patient. So don't be afraid and get your queries cleared by your anasthesitist.
Hope you have got your answers.