I would not be too concerned about earthworms leading to parasite infections. It happens with pinkies as well and I've seen it with crickets so the risk is always there. The place I work has been feeding many of its animals, including snakes, earthworms as part of a larger diet for many years and it has never caused problems.
My understanding of the Greensnake you are talking about is that unlike its close relative, the Smooth Greensnake, it is more arboreal and does not feed on insects as much. Earthworms seem to make up a large proportion of its natural diet and captive animals have done just fine on earthworms alone. Caterpillars and other soft-bodied insects have been taken as well. I've heard though that it's a pretty difficult species to keep in captivity. I do not know if any are being captive bred but if so then that's your best bet. Wild-caught are available but it would be harder to get them to start eating.
It's sort of ironic -- I had never heard anybody mention this species on the kingsnake boards until this past december and now here it is coming up again. Somebody recently posted it on the "snakes -- what kind" forum. According to him he bought some at a petshop as an unitdentified greensnake species and that they employees claimed they had not eaten in a month. He was able to feed it when it opened its mouth in defense though. They should be pretty docile. I've handled a few in the wild and they never showed any intent to strike.