17:11 reads "For the life of the flesh is in the blood, and I have assigned it to you for making expiation for your lives upon the altar; it is the blood, as life, that effects expiation."
That is an explanation as to why eating blood is forbidden in 17:10, because blood has a special place in that for those sacrifices that use animals, it is the blood which brings about the atonement. Lev 4 is talking about a sacrifice for atonement that has no blood.
That is quite different from the claim that "without the shedding of blood there is no remission of sin" which is what you report from Hebrews. It clearly isn't quoting from Leviticus because no where in Leviticus is there any statement about an absolute need for there to be blood.