I am not aware of any alternative to putting a hernia right in adults other than surgery or just living with it. The problem with the latter can be that they never get better and can only worsen, sometimes leading to intestinal strangulation.
I do know there are alternative surgery techniques to the mesh. You might try getting some info from the shouldice clinic in Canada. They have a pretty good reputation and have a surgical technique that mends umbilical hernias and in most cases (as I understand it) they do not use mesh, but a process instead involving what I believe is a very thin steel thread and a special technique.
You can find out more at their site which you can search with their name.