How can I transfer USD from one brokerage to another brokerage without incurring any exchange fee?

It depends on your brokerage. For example, if you use Tiger Brokers or Moomoo, they offer free USD deposits and withdrawals with DBS multicurrency accounts. You can then use DBS Remit to transfer the USD to another brokerage's USD account in the US for free.

If you are a DBS Treasures customer, you can receive a USD deposit by wire transfer to a multicurrency account at no extra cost, but would otherwise cost $10.

You can also consider transfering your holdings instead of selling. Some brokers also allow partial account transfers using ACATS, but you need to check with your broker for the details and costs. Interactive Brokers and TD Ameritrade do not charge for partial ACATS transfers.​​​

I did that before during my transfer of usd from fsmone to tiger broker without incurring additional fee. But it depends on which broker to and from are you transfering.