Jesus blood had to PAY for SIN and Mary blood could not !!
If some of her blood, at the time of birth, got loose from her and got into Jesus, that blood and its cells would not have lasted for thirty years. Blood cells last a while and then they are broken down in the liver and materials are recycled and there is blood cell breakdown waste which goes out through the bile . . . if I remember right. So, her blood would not have been His blood, by the time Jesus died for our sins, shedding His blood for us.
But, even if some of Mary's blood, in theory, was still present when Jesus shed His blood for us, it would not make any difference. Because who and how Jesus is decides if His blood is holy. Even if her cells were in His blood, His blood still would be His blood!
He ate food that we ate, and food eaten gets into the blood, after being digested. And it is used to manufacture blood cells and fluids. So, Jesus' blood was made from what humans use to manufacture blood. This does not mean Jesus had unholy blood. But because Jesus is holy, His blood is holy. What is used to make it does not decide, but it is determined by God.
So, I can see, it is not what went into Jesus and His blood, which decided if He is holy and if His blood is holy, but what is in Jesus Himself, spiritually, decided. The whipping, I would say, drove dirt and bacteria into Jesus' body and into His blood, but that did not make His blood unholy.
So, likewise, even if Joseph had been one with Mary in begetting Jesus in her womb, Jesus who is spiritual by nature is incapable of being corrupted by sin > James 1:13. The Holy Spirit and Jesus would have resisted any evil spirit sin stuff. And, likewise, Mary could not give Jesus any wrong spirit stuff.
So, this can be good to know > how Jesus in us can not be overcome and contaminated by our sin. Plus, Jesus growing in us makes us more and more immune to sin-sicknesses > as we are matured in His sin-incapable love > 1 John 4:17-18 > Galatians 4:19.
"You are of God, little children, and have overcome them, because He who is in you is greater than he who is in the world." (1 John 4:4)