The Targum of וַיְשַׁלַּח as וְשַׁלַּח

In Targum Onkelos on Balak, we read:

כב,מ וַיִּזְבַּח בָּלָק, בָּקָר וָצֹאן; וַיְשַׁלַּח לְבִלְעָם, וְלַשָּׂרִים אֲשֶׁר אִתּוֹ.

וּנְכַס בָּלָק, תּוֹרִין וְעָן; וְשַׁלַּח לְבִלְעָם, וּלְרַבְרְבַיָּא דְּעִמֵּיהּ.

Ohev Ger writes of a variant girsa recorded in the sefer haAruch:

"וְשַׁלַּח   {so יא"ר קע"א, and יוני, ש"ח and סביוניטה}, and so testified the Meturgeman {=R' Eliyahu Bachur} that he found in all the sefarim. And the girsa of the Aruch is ושדר, and after him most printers. But the author of sefer יא"ר brings a masorah on the pasuk of הנה שלחתי הגדי הזה, as follows: 'there are two which are translated with the language of שדרא, namely וישלח יהודה and this one'. And perhaps this is a scribal error which fell into the Aruch, that someone wrote וישלח לבלעם in place of וישלח יהודה. Or else that the intent of the Aruch was to Targum Yerushalmi, for the Targum which is ascribed to Yonatan is ושדר."

Here is one such printed text, in our Mikraos Gedolos, with ושדר. See Targum Pseudo-Yonatan on this pasuk here.

Here is Meturgeman on Shalach. And on Shadar:

As you can see, Meturgeman has an additional proof, that the binyan of kal produces שדר while the binyan of pael {such as in וַיְשַׁלַּח} does not.

Perhaps what was going through people's minds was sending messengers vs. sending an object. When you send messengers on a mission you are sending shluchim, agents. Whereas the instances in which Yehuda sends, he is sending an object. What is being sent? A message? Or the בָּקָר וָצֹאן which Balak had slaughtered? Of course, this is not so. See how וישלח occurs.

One more point, to tie it in to a recent post. I recently discussed how Targum Yonasan is really Targum Pseudo-Yonatan, and therefore how a reference to Constantina is not evidence of prophetic foreknowledge in the Jewish Oral tradition, but rather a simple reference to a known place. Shadal, above, refers to this Targum as תרגום ירושלמי, כי בתרגום המכונה ליונתן ושדר. Thus, Shadal agrees that is is Pseudo-Yonatan.