I think it is as easy as you suspect.
Hebrews does focus on the superiority of the New Covenant a little more from the ceremonial perspective than does some of the other Epistles, as this had more meaning to a Jewish audience. However this superiority of the blood of Christ, versus blood of bulls only has meaning as it satisfies the moral demands of the broken laws under the Mosaic Law. So it would be untrue to think any other covenant was being referred to besides the Mosaic Covenant, as that is the only Old Covenant there is. It is the condemnation of the Mosaic moral law specifically that Jesus the High Priest has removed. Jesus, by offering his own body and soul upon an altar, removed the curse of the law, whereby he was so pleasing to God that he was ‘raised up’, higher than the angels that we might rest in forgiveness forever. This is absolutely what Hebrews argues at length by various convincing arguments tailored to a Jewish audience.
The Old Covenant is the covenant God made with Israel under Moses often called the Mosaic Covenant. It was an agreement between God and Israel that they would vow to keep all the commands provided by Moses. These laws include all those laws recorded in the first five books of the Bible and summarized under the Ten Commandments. Ceremonially the highest point of this law was the high priest and all his functions.
As this is the case we find the tablets actually called the 'covenant laws':
As the Lord commanded Moses, Aaron put the manna with the tablets of the covenant law, so that it might be preserved. (Exodus 16:34, NIV)
As the Priesthood was fully integrated with the commands and equally part of that covenant it was ratified in blood: (This is a 'Ah..there it is' location.)
Moses took half of the blood and put it in bowls, and the other half he splashed against the altar. Then he took the Book of the Covenant and read it to the people. They responded, “We will do everything the Lord has said; we will obey.” Moses then took the blood, sprinkled it on the people and said, “This is the blood of the covenant that the Lord has made with you in accordance with all these words.” (Exodus 24:6-9, NIV)
Naturally in Hebrews when referring to the Old Covenant both the commands and ceremonies are involved. First respecting ceremonial the Covenants are compared:
The blood of goats and bulls and the ashes of a heifer sprinkled on those who are ceremonially unclean sanctify them so that they are outwardly clean. How much more, then, will the blood of Christ, who through the eternal Spirit offered himself unblemished to God, cleanse our consciences from acts that lead to death, so that we may serve the living God!
For this reason Christ is the mediator of a new covenant, that those who are called may receive the promised eternal inheritance —now that he has died as a ransom to set them free from the sins committed under the first covenant. (Hebrews 9:13-15, NIV)
Second respecting the commands, the Covenants are compared:
Now if the ministry that brought death, which was engraved in letters on stone, came with glory, so that the Israelites could not look steadily at the face of Moses because of its glory, transitory though it was, will not the ministry of the Spirit be even more glorious? If the ministry that brought condemnation was glorious, how much more glorious is the ministry that brings righteousness! For what was glorious has no glory now in comparison with the surpassing glory. And if what was transitory came with glory, how much greater is the glory of that which lasts! (2 Corinthians 3:7-11, NIV)
This is the covenant I will establish with the people of Israel after that time, declares the Lord. I will put my laws in their minds and write them on their hearts. I will be their God, and they will be my people. (Hebrews 8:10, NIV)
Of course the Old Covenant also included the theocracy, as God was a citizen as it were of Israel and its civil King. This also is included in the Old Covenant and is superseded by the New:
For he himself is our peace, who has made the two groups one and has destroyed the barrier, the dividing wall of hostility, by setting aside in his flesh the law with its commands and regulations. His purpose was to create in himself one new humanity out of the two, thus making peace (Ephesians 2:14-15, NIV)
This is the Old Covenant the writer of Hebrews refers to, the entire Mosaic Law.