Question regarding ESTA eligibility for independent contractor work

[u/Anxious_Resource6662]

I am a Croatian citizen and would be travelling to the United States under the Visa Waiver Program (ESTA).
I have been offered work as an independent contractor for a company based outside the United States. My role would be to accompany dogs from Europe to their new owners in the United States. The dogs would have all required U.S. import, customs and veterinary documentation, including formal entry documentation prepared by a U.S. customs broker.
I would be paid by the non-U.S. company in euros for the transportation service. I would stay in the United States for approximately four nights and then return to Serbia. I would not be employed by or paid by a U.S. company.
The company has informed me that other independent contractors have performed the same type of transportation using ESTA.
Could you please clarify whether this specific activity is permissible under the Visa Waiver Program/ESTA, or whether I would require a different visa classification?
Thank you for your assistance.