Is it fair to say that the sacrifices in the Old Testament never took away sins, as Hebrews 10:4 says, but rather held back the consequences of it until Jesus came as the perfect sacrifice to finally atone for sins?
This is not exactly how I would put it, but it is pretty close. What I would say is that the sacrifices under the Mosaic system did a few things. They prepared the way for us to understand the sacrifice of Jesus. They served as foreshadows that explained the sacrifice of Christ. Jesus fulfilled the law (Matthew 5:17), but there needed to be a law for Jesus to fulfill.
They also demonstrated the seriousness of sin. In the words of Paul, the sacrifices and the law “made sin utterly sinful.” (Romans 7:13). The law was brought in so that trespass might increase (Romans 5:20). Through these sacrifices the Jews (and we) began to understand the seriousness of sin and that sin required blood/death.
Perhaps most importantly for the Jews, the sin and guilt offerings created “ceremonial cleanness.” (Leviticus 22:4-9, Hebrews 9:13-14) In other words they dealt with sin to the point that the Jews could come and worship God acceptably. This outward cleanness was not the ultimate removal of sin, but the covering up of sin to the point that they could be the people of God and live in fellowship with him, so that he could dwell with them. It was a kind of provisional forgiveness, not an absolute forgiveness. This was no small thing, because it made the Jews a special people of God.
Whether these sacrifices “held back” the consequences of sin is debatable. The Jews certainly suffered some consequences for their sins. So, I agree with the concept you are describing, but thing that there are better ways to express this idea.