How does cutting Sils work? (For those without Angrist)

[NotMorgoth]

I've managed to get several wins now. The first one found Angrist and cut a Silmaril from the crown easily, but the second did not, and had a harder time.

My main weapon was a longsword and I did not have any success cutting the Sil with this; I then tried switching to a 5d3 mattock, which, with a strength potion cut the Sil on the first attempt.

So is it just a case of getting the highest damage weapon possible? Would a great axe or similar be just as good? How much does melee skill contribute to success chance, and is it much harder for low-melee characters, eg archers or pacifists?

I gather that in the Elder Days it was possible to use Song of Sharpness with a light weapon, but that song is long forgotten and has passed away into the West.