Your premise that the 10 Commandments aren't part of the Old Covenant, is incorrect. In fact, the 10 Commandments are called the stones or tablets of the Covenant.
[A.] Exo 19:3 And Moses went up unto God, and the LORD called unto him out of the mountain, saying, Thus shalt thou say to the house of Jacob, and tell the children of Israel;
Exo 19:4 Ye have seen what I did unto the Egyptians, and how I bare you on eagles' wings, and brought you unto myself.
Exo 19:5 Now therefore, if ye will obey my voice indeed, and keep my covenant, then ye shall be a peculiar treasure unto me above all people: for all the earth is mine:
Exo 19:6 And ye shall be unto me a kingdom of priests, and an holy nation. These are the words which thou shalt speak unto the children of Israel.
Exo 19:7 And Moses came and called for the elders of the people, and laid before their faces all these words which the LORD commanded him.
Exo 19:8 And all the people answered together, and said, All that the LORD hath spoken we will do. And Moses returned the words of the people unto the LORD.
Exo 19:9 And the LORD said unto Moses, Lo, I come unto thee in a thick cloud, that the people may hear when I speak with thee, and believe thee for ever. And Moses told the words of the people unto the LORD.
Exo 19:10 And the LORD said unto Moses, Go unto the people, and sanctify them to day and to morrow, and let them wash their clothes,
Exo 19:11 And be ready against the third day: for the third day the LORD will come down in the sight of all the people upon mount Sinai.
[B.] Exo 24:2 And Moses alone shall come near the LORD: but they shall not come nigh; neither shall the people go up with him.
Exo 24:3 And Moses came and told the people all the words of the LORD, and all the judgments: and all the people answered with one voice, and said, All the words which the LORD hath said will we do.
Exo 24:4 And Moses wrote all the words of the LORD, and rose up early in the morning, and builded an altar under the hill, and twelve pillars, according to the twelve tribes of Israel.
Exo 24:5 And he sent young men of the children of Israel, which offered burnt offerings, and sacrificed peace offerings of oxen unto the LORD.
Exo 24:6 And Moses took half of the blood, and put it in basons; and half of the blood he sprinkled on the altar.
Exo 24:7 And he took the book of the covenant, and read in the audience of the people: and they said, All that the LORD hath said will we do, and be obedient.
Exo 24:8 And Moses took the blood, and sprinkled it on the people, and said, Behold the blood of the covenant, which the LORD hath made with you concerning all these words.
Exo 24:9 Then went up Moses, and Aaron, Nadab, and Abihu, and seventy of the elders of Israel:
Exo 24:10 And they saw the God of Israel: and there was under his feet as it were a paved work of a sapphire stone, and as it were the body of heaven in his clearness.
Exo 24:11 And upon the nobles of the children of Israel he laid not his hand: also they saw God, and did eat and drink. (“the Old” Covenant meal on the mountain, just like at the Last Supper with Jesus on the mountain where Jerusalem sat, in the New Covenant; Mat. 26:28; Mar. 14:24; Luk. 22:20; 1 Cor. 11:25)
[C.] Exo 34:10 And he said, Behold, I make a covenant: before all thy people I will do marvels, such as have not been done in all the earth, nor in any nation: and all the people among which thou art shall see the work of the LORD: for it is a terrible thing that I will do with thee.
Exo 34:11 Observe thou that which I command thee this day: behold, I drive out before thee the Amorite, and the Canaanite, and the Hittite, and the Perizzite, and the Hivite, and the Jebusite.
Exo 34:12 Take heed to thyself, lest thou make a covenant with the inhabitants of the land whither thou goest, lest it be for a snare in the midst of thee:
Exo 34:13 But ye shall destroy their altars, break their images, and cut down their groves:
Exo 34:14 For thou shalt worship no other god: for the LORD, whose name is Jealous, is a jealous God:
Exo 34:15 Lest thou make a covenant with the inhabitants of the land, and they go a whoring after their gods, and do sacrifice unto their gods, and one call thee, and thou eat of his sacrifice;
Exo 34:16 And thou take of their daughters unto thy sons, and their daughters go a whoring after their gods, and make thy sons go a whoring after their gods.
Exo 34:17 Thou shalt make thee no molten gods.
Exo 34:18 The feast of unleavened bread shalt thou keep. Seven days thou shalt eat unleavened bread, as I commanded thee, in the time of the month Abib: for in the month Abib thou camest out from Egypt.
Exo 34:19 All that openeth the matrix is mine; and every firstling among thy cattle, whether ox or sheep, that is male.
Exo 34:20 But the firstling of an ass thou shalt redeem with a lamb: and if thou redeem him not, then shalt thou break his neck. All the firstborn of thy sons thou shalt redeem. And none shall appear before me empty.
Exo 34:21 Six days thou shalt work, but on the seventh day thou shalt rest: in earing time and in harvest thou shalt rest.
Exo 34:22 And thou shalt observe the feast of weeks, of the firstfruits of wheat harvest, and the feast of ingathering at the year's end.
Exo 34:23 Thrice in the year shall all your men children appear before the Lord GOD, the God of Israel.
Exo 34:24 For I will cast out the nations before thee, and enlarge thy borders: neither shall any man desire thy land, when thou shalt go up to appear before the LORD thy God thrice in the year.
Exo 34:25 Thou shalt not offer the blood of my sacrifice with leaven; neither shall the sacrifice of the feast of the passover be left unto the morning.
Exo 34:26 The first of the firstfruits of thy land thou shalt bring unto the house of the LORD thy God. Thou shalt not seethe a kid in his mother's milk.
Exo 34:27 And the LORD said unto Moses, Write thou these words: for after the tenor of these words I have made a covenant with thee and with Israel.