Hashem told us to erase the memory of Amalek but its up to us which method we use. We can let someone else do the dirty work, we can let him convert or intermarry. I didnt see anywhere that says that Hashem wants Amalek dead, gone doesnt mean dead.
Exactly where does it say that you are not allowed to cause yourself to bleed?
Breishis 9:5 – I will demand (an account) for your blood and for your souls.
Rashi- your blood – refers to one who sheds his own blood.
Rashi- your souls – refers to someone who strangles himself even though no blood was spilled.
(For Wolf – “sheds blood” is not the same as allowing blood to come out during brushing teeth and so on)
So this is one of the mitzvahs bnei noach and applies to goim and Jews alike. Practically this means goim cant get a bris milah. And thats why Avraham couldnt do it before he was specifically commanded to do it.