I do a lot of rock climbing as well so know Langdale very well, Gimmer crag to the right of Pike O Stickle is probably my favourite crag, I've been meaning to nip over and get some greenstone but from what I can gather is isn't knappable.
It's perhaps not as easy to knap as flint but it's still workable and for the likes of the tools you're talking about it's good stuff.
It comes in different types. There's large grained where the green is a pale uniform green/grey. It weathers to purple on the outside and you'll see a lot of it when you get there. Not much cop, don't waste your time with it, seems to prefer breaking at right angles rather than flaking properly.
Then there's the dark green. Weathers to white. It's what the polished axes were ground down from. Smaller grained and not bad at all for percussion flaking. Never tried pressure flaking it but then I'm not very good at pressure flaking anyway so it wouldn't be a good gauge.
Makes very good scrapers, holds it's edge well when working wood.
I'd say it's on a par with good basalt.
I stuck up a picture of some once, hang on:
http://www.bushcraftuk.com/forum/showthread.php?t=16315
You can see on the left of the lump where I'd been knocking off flakes.
Then there's fine grained. It's pale again but more of a washed out jade colour - still has a slight richness to the colour. Weathers white again and the lumps I found had white seams through it that didn't affect the way it flaked. Quite pretty stuff. Flakes as well as anything I've ever tried, percussive and pressure. Should be just the job for your arrowheads.
The bulk of greenstone finds may have been polished celts but celts are made that way because the shape takes abuse well. Knapped axes have all those changes in thickness, leftover weak spot and ridges for shock waves to ride along. Celts will last a lot longer without damage so it was worth putting in the extra effort.
The rock itself is still knappable though.
Man I always end up prattling on on these threads. Sorry, hope some of that is of use.