Can I transfer some BTC with 0 tx fee now, when the mempool is empty?

I wanna send a tiny amount of BTC (0.001BTC). I am not in a hurry and I noticed the mempool is sometimes empty these days because the market is cold. So can I set the network fee to 1sat/byte or even zero?

Will miners add my zero-fee tx to the new block when the mempool is empty?

Thank you.