How can we offer Jesus' Body, Blood, Soul and Divinity in the Divine Mercy Chaplet?
The short answer
Saying the prayer isn't offering Mass. But because Christ made his one sacrifice for us, that perfect prayer is now ours, and we can always refer to it. In effect we say to the Father: "By the merits of his Passion, have mercy."
Not the Mass
At Mass we participate in Christ's one sacrifice. Praying the chaplet is not the same.
His prayer is ours
Because Christ made that sacrifice, it is now ours and we can always appeal to it. It is powerful because it is his prayer. Essentially we are saying: Father, by the merits of his Passion, we ask your mercy.