Will a service that can transfer liquid assets (on blockchain like Ethereum) without any transactions be considered a mixer?

No because nobody uses those kind of liquid assets for money laundering.

I would like to receive an answer from the administrator. I plan to post the smart contract address for testing. I don't want to take risks.

In that case, I recommend you PM theymos directly to get a speedy reply. He is probably not monitoring this old thread anymore.

Thanks for the advice! I will do this before publishing the smart contract address on the test network.