dilute DMSO or saline are considered the standards for vehicles. I would refer to the following research gate post for more information:

https://www.researchgate.net/post/Is_it_a_good_idea_to_inject_DMSO-dissolved_drugs_to_mice_intraperitoneally

I think the best vehicle for arachidonic acid for IP injections in mice is mice serum albumin (MSA).

Preparation of fatty acid-MSA complex

In brief, arachidonic acid is dissolved in ethanol:H2O (1:1, vol:vol) at 37°C at a final concentration of 150 mmol/l. Aliquots of stock solutions were complexed with fatty acid-free MSA (10% solution in H2O) by stirring for 1 h at 37°C and then diluted in order to adjust the final molar ratio ofarachidonic acid:BSA at 5:1 and ethanol concentration at less than 0.33% (vol/vol).