The “whole Law” is given to Moses beginning in verse 31, the Decalogue is a sort of constitution that informs all the rest of the detailed legislation that follows (and yes, within the Law the Ten Commandments stand out). But in Deut. 5:31 God is giving Moses not “all the commands” but literally “the whole command” or the whole substance of the law considered as a single entity (kol-hammiṣwâ is singular). Keeping the “whole command” is directed to walking in the way Yahweh commands. Here Moses is given the whole law, not just details of specific legislation (decrees and laws).
In other words, the statement that Jesus has summarized the Ten Commandments is backwards. Jesus is actually responding with the whole command from which the Decalogue is derived.
Deut. 5:30 Go and say to them, “Return to your tents.” 31 But you, stand here by me, and I will tell you the whole commandment and the statutes and the rules that you shall teach them, that they may do them in the land that I am giving them to possess.’ 32 You shall be careful therefore to do as the LORD your God has commanded you. You shall not turn aside to the right hand or to the left. 33 You shall walk in all the way that the LORD your God has commanded you, that you may live, and that it may go well with you, and that you may live long in the land that you shall possess. 6:1 “Now this is the commandment—the statutes and the rules—that the LORD your God commanded me to teach you, that you may do them in the land to which you are going over, to possess it, 2 that you may fear the LORD your God, you and your son and your son’s son, by keeping all his statutes and his commandments, which I command you, all the days of your life, and that your days may be long. 3 Hear therefore, O Israel, and be careful to do them, that it may go well with you, and that you may multiply greatly, as the LORD, the God of your fathers, has promised you, in a land flowing with milk and honey. 4 “Hear, O Israel: The LORD our God, the LORD is one. 5 You shall love the LORD your God with all your heart and with all your soul and with all your might.
Within the topic of the OP, however, we are drifting with this argument. What is being asked is if we should use the Law in evangelism. And it depends on the context of its usage. As an example I don't think anyone would object (God's transcendence, his perfect nature, and man's fallen status are illustrated through the Law). But in terms of putting people "under the Law" (even if we conclude we are speaking of only the Ten Commandments), what needs to be shown are that people are actually under the authority of the law, or the Decalogue (which is by definition binding). I am willing to grant for arguments sake (and to stay on target) that the Ten Commandments are given before the Law and separate from the Law (a concession for the sake of argument,dismissed with prejudice). What still needs to be shown is how the world is included in this covenant.