Is there a concern of 'you and not strangers' in the blessing of the children?

We have the custom that the father blesses the children on Friday night with 'May God make you...' and 'May the Lord bless you and keep you.' The question is whether there is a concern of 'you and not strangers'?

Continue the custom, and it is preferable to intend explicitly not for the fulfillment of the commandment of the Priestly Blessing, or to place one hand.

Gemara in Ketubot 24: and these are the words: 'They asked, what is the law regarding raising for lineage from the lifting of hands, ask according to the one who says we raise from terumah for lineage, and ask according to the one who says we do not raise, ask according to the one who says we raise, these words apply to terumah which is a sin of death, but the lifting of hands which is a prohibition, not or perhaps there is no difference, etc.' And in Rashi there, in the commentary 'that it is a prohibition': 'Thus shall you bless, you and not strangers, and a negative derived from a positive is a positive.' And in Tosafot on Shabbat, page 118: wrote 'R"I did not know what prohibition there is for a stranger ascending to the platform, if not because of a blessing in vain, that the Torah said for the priests to bless Israel.' And the Rema at the beginning of Siman 128 remained on the words of R"I in difficulty from the Gemara in Ketubot 24:, and wrote that perhaps R"I did not say there is no prohibition, except for one ascending with other priests. And in Magen Avraham rejected this distinction and brought the explanation of the Maharsha that there is no prohibition to say the blessing 'May He bless you' without the blessing 'Who sanctified us with His commandments'. Nevertheless, in the Mishnah Berurah Siman 128 S"K 6, it is written that a stranger who blesses transgresses a positive commandment. However, in Biur Halacha in the commentary 'that a stranger' on the custom of the world to bless a friend with 'May He bless you', relying on the opinion of the Bach that transgresses a positive commandment only in the lifting of hands, or because the sages decreed not to lift hands except in prayer, again one who blesses thus clearly shows that he does not intend for the commandment, and does not transgress a positive commandment, especially if it is said that commandments require intention, and he did not intend for the commandment. And another explanation I heard, that since there is no lifting of hands at night as written in the Mishnah Berurah, therefore it certainly does not apply to 'you and not strangers', for even the priests on Friday night cannot fulfill the Priestly Blessing. And in the Siddur of the Gra, part 2, Siman 87, it is written because of this question, not to place both hands on the child but only one hand.