There are 3 avataras, I can think of which does not include war,
While Vamana avatar was to restore the authority of Indra over the heavens, in Vyasa avatar Lord Vishnu divided Vedas in four parts.
SB 8.22.31 — The Lord continued: Because of his great tolerance, I have given him a place not obtainable even by the demigods. He will become King of the heavenly planets during the period of the Manu known as Sāvarṇi.
SB 8.22.32 — Until Bali Mahārāja achieves the position of King of heaven, he shall live on the planet Sutala, which was made by Viśvakarmā according to My order. Because it is especially protected by Me, it is free from mental and bodily miseries, fatigue, dizziness, defeat and all other disturbances. Bali Mahārāja, you may now go live there peacefully.
SB 8.22.33 — O Bali Mahārāja [Indrasena], now you may go to the planet Sutala, which is desired even by the demigods. Live there peacefully, surrounded by your friends and relatives. All good fortune unto you.
Ref: vedabase SB 8.22
In every Dwápara (or third) age, Vishńu, in the person of Vyása, in order to promote the good of mankind, divides the Veda, which is properly but one, into many portions: observing the limited perseverance, energy, and application of mortals, he makes the Veda fourfold, to adapt it to their capacities; and the bodily form which he assumes, in order to effect that classification, is known by the name of Veda-vyása. Of the different Vyásas in the present Manwantara, and the branches which they have taught, you shall have an account.
Ref: Vishnu Purana Book 3, Chapter 3.
One more avatar was Kurma avatar, in this avatar Lord Vishnu helped Gods and Demons to support the foundation of Mandara Mountain for Samudra Manthan.
tam utthitaṁ vīkṣya kulācalaṁ punaḥ
samudyatā nirmathituṁ surāsurāḥ
dadhāra pṛṣṭhena sa lakṣa-yojana-
prastāriṇā dvīpa ivāparo mahān
When the demigods and demons saw that Mandara Mountain had been lifted, they were enlivened and encouraged to begin churning again. The mountain rested on the back of the great tortoise, which extended for eight hundred thousand miles like a large island. [SB 8.7.9]
paribhramantaṁ girim aṅga pṛṣṭhataḥ
bibhrat tad-āvartanam ādi-kacchapo
mene ’ṅga-kaṇḍūyanam aprameyaḥ
O King, when the demigods and demons, by the strength of their arms, rotated Mandara Mountain on the back of the extraordinary tortoise, the tortoise accepted the rolling of the mountain as a means of scratching His body, and thus He felt a pleasing sensation. [SB 8.7.10]
Reference Bhagavatam Canto 8 chapter 7