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There dosen't seem to be any "secret message" as sent by Dhṛtarāṣṭra for Arjuna.

This is what we get from the Book 5: Udyoga Parva, Section XXII.

"Dhritarashtra said, 'They say, O Sanjaya, that the Pandavas have arrived at Upaplavya. Go thou and enquire after them.

Thou must greet Ajatasatru (i.e. Yudhiṣṭhira) in the following words- 'By good luck it is that (emerged from the woods) thou hast reached such a city. And to all of them thou must say, O Sanjaya, these words. Are ye well, having spent that harassing period of sojourn, ye who were unworthy of such harassment?'.

In no time will they be appeased towards us, for though treated treacherously (by foes), yet they are righteous and good. In no case, O Sanjaya, have I ever met with any untruthfulness on the part of the Pandavas. It was by their own valour that they had won all their prosperity, and (yet) they were ever dutiful to me.

Though I scrutinized their conduct, I could never find fault with them,--no, not even a single fault for which we might blame them. They always act mindful of virtue and wealth; they never give way to love of sensual enjoyments, or cold, or hunger, or thirst; they subdue steep and laziness and wrath and joy and heedlessness. The sons of Pritha, mindful of both virtue and wealth, are ever pleasant to all. On proper occasions they part with their wealth to friends. Friendship with them never loses its ardour on account of length of time; for they bestow honours and wealth on every one according to his deserts. Not a soul in the race of Ajamida ever entertains hatred for them excepting this vile, capricious, dull-headed Duryodhana, and excepting also the still more mean-minded Karna. These two always enhance the energy of those high-souled ones who have been divested of both friends and happiness. Enterprising and brought up in every indulgence, Duryodhana reckons all that to be well-done. It is childish on Duryodhana's part to think that it is possible to rob the Pandavas of their just share so long as they are alive. It is wise to yield to Yudhishthira his due share before the war,--to him whose steps are followed by Arjuna and Krishna and Bhima and Satyaki and the two sons of Madri and the warriors of the Srinjaya race........
[p. 36]
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[p. 37]

The son of Kunti and Pandu, Yudhishthira, is virtuous and brave and eschews deeds that bring on shame. Endued with great energy, he hath been wronged by Duryodhana. If he were not high-minded, the would in wrath burn the Dhritarashtras. I do not so much dread Arjuna or Bhima or Krishna or the twin brothers as I dread the wrath of the king,* O Suta, when his wrath is excited. His austerities are great; he is devoted to Brahmacharya practices. His heart's wishes will certainly be fulfilled. When I think of his wrath, O Sanjaya, and consider how just it is, I am filled with alarm.

Go thou speedily on a car, despatched by me, where the troops of the king of the Panchalas are encamped. Thou wilt ask Yudhishthira about his welfare. Thou wilt repeatedly address him in affectionate terms. Thou wilt also meet Krishna, O child, who is the chief of all brave men and who is endued with a magnanimous soul. Him also thou wilt ask on my part as to his welfare, and tell him that Dhritarashtra is desirous of peace with Pandu's sons. O Suta, there is nothing that Yudhishthira, the son of Kunti, would not do at the bidding of Krishna. Kesava is as dear to them as their own selves. Possessed of great learning, he is ever devoted to their cause. Thou wilt also enquire about the welfare of all the assembled sons of Pandu and the Srinjayas and Satyaki and Virata and all the five sons of Draupadi, professing to be a messenger from me. And whatsoever also thou mayst deem to be opportune, and beneficial for the Bharata race, all that, O Sanjaya, thou must say in the midst of those kings,--everything, in sooth, that may not be unpalatable or provocative of war.'

[p. 38]

Thus, this "Peace Meassage" from Dhṛtarāṣṭra more of looks like an "emotional-blackmail" technique, aimed at taking advantage of the extremely Dharma adhering nature of the Pāṇḍavas (especially Yudhiṣṭhira, since everyone is bound to follow him since he's the King and also the eldest). Also, from the above texts, it's kind of clear that Dhṛtarāṣṭra is more afraid of Yudhiṣṭhira, than any of his brother or people in the court (not even even Śhrī Kṛiṣhṇa)

tl;dr

Therefore, the message (from Dhṛtarāṣṭra) is aimed for everyone in the court of Yudhiṣṭhira and not just some "secret message" specifically for Arjuna. Aim of the message is to collectively "black-mail" Pāṇḍavas in the name of Dharma and "blood-relationship", so that either:

• They take back their foot from the upcoming war, (or)
• They are shaken sentimentally and pschologically (thus their performance in the war will reduce).