I gather from your description that it is an umbilical hernia.....I may be wrong. Anyway mesh would strengthen the hernia, but there are problems with mesh repair that one doesn't see with non-mesh repairs e.g infection.
You may well be a difficult case as you have had previous abdominal surgery. If you you have laparoscopic repair it will ALWAYS be done under G.A (knocked out) but if it is done without mesh and without laparoscopy, it may be done under local.
I have made many assumptions here, so could you tell me what type of hernia it is.