Fr. Michalenko and the MIC are the official promoters of the Divine Mercy.
Their official website for the Divine Mercy devotion, including the chaplet, is Thedivinemercy.org which is linked to their Marian Fathers website Marian.org .
They have instructions for praying the chaplet here:
The wording of the prayer on their website, from the above link is,
Eternal Father, I offer you the Body and Blood, Soul and Divinity of Your Dearly Beloved Son, Our Lord, Jesus Christ, in atonement for our sins and those of the whole world.
I have never heard any prayer group use a wording other than this. I have also personally prayed the chaplet more than once in a group led by MIC Fr. Calloway and he used the above wording.
I think you should just use the wording the Marian Fathers have on their website, and stop worrying about this, as you don’t seem to have a reliable source saying otherwise, and also, the Marian Fathers are not going to promulgate a wrong way of saying the prayer they promote on their very own website.