Even in Somayajña like Agniṣṭoma the method used to kill the animal is strangulation.
As Julius Eggeling notes in the Introduction to his translation of Śatapatha Brāhmaṇa, kāṇḍas 3 and 4 deal with Somayajña:
The contents of the third and fourth books of the Śatapatha-brāhmaṇa form an important chapter of its dogmatic explanation of the sacrificial ceremonial. This portion of the work treats of the ordinary forms of the most sacred of Vedic sacrificial rites, the 'Soma-sacrifice.' The exposition of the Soma-ritual also includes an account of the animal offering which, though it may be performed as an independent sacrifice, more usually constitutes an integral part of the Saumya-adhvara.
From Kāṇḍa III, Adhyāya 8, Brāhmaṇa 1:
They then step back (to the altar) and sit down turning towards the Āhavanīya, 'lest they should be eye-witnesses to its being quieted (strangled).' They do not slay it on the frontal bone, for that is human manner; nor behind the ear, for that is after the manner of the Fathers. They either choke it by merely keeping its mouth closed, or they make a noose. Therefore he says not, 'Slay! kill!' for that is human manner, but, 'Quiet it! It has passed away!' for that is after the manner of the gods. For when he says, 'It has passed away,' then this one (the Sacrificer) passes away to the gods: therefore he says, 'It has passed away.'
When they hold it down, then, before the strangling, he offers with 'Hail, to the gods!' And when (the butcher) says, 'Quieted is the victim,' he offers with, 'To the gods, Hail!' Thus some of the gods are preceded by 'Hail,' and others followed by 'Hail;' he thereby gratifies them, and thus gratified both kinds of gods convey him to the heavenly world. These are the so-called 'paripaśavya' oblations; he may offer them if he choose; or, if he choose, he need not mind them.