When I had my hydroponics I used 25mm self tapping countersunk head screws.
They were only screwed in halfway so the mesh could be pulled over them.
It did make a little hole but I never found the hole to get bigger unless I was lazy with positioning the mesh.
In your garden the screws would be located under the sill around top of the bed so you don't catch clothing, etc on them but can still pull the mesh down a little & hook over the screw head.
The mesh held through even the worst storms & strongest wind.
They were only screwed in halfway so the mesh could be pulled over them.
It did make a little hole but I never found the hole to get bigger unless I was lazy with positioning the mesh.
In your garden the screws would be located under the sill around top of the bed so you don't catch clothing, etc on them but can still pull the mesh down a little & hook over the screw head.
The mesh held through even the worst storms & strongest wind.