Can a 3.3V FTDI serial cable burn hikey UART pins?

No.
TX and RX carry signals at 3.3v or higher. This is OUTSIDE OF SPEC and could DAMAGE YOUR BOARD.

I’m not aware of ANY board that is “specific to hikey”. The UART mezzanine is compatible with ALL 96boards devices.

And I’m not quite sure why you object to the audio mezzanine. The only feature of that board that is limited to dragonboard is the audio, which will not hinder the rest of the functionality of the board on non-dragonboard SBCs. And for $5 with free shipping, you can’t go wrong with it.

Indeed. This has grown into a surprisingly complex thread given the answer to the question in the subject title can be given in one word (“yes”).

So, for clarity (and especially for future readers of this thread):

When working with TTL UARTs then the TX pin will be at logic 1 when the transmitter is idle. That means you can attach a voltmeter to it. If you are working with an unknown (or otherwise suspect) USB <-> UART device then measure the voltage on the TX pin. If it is much greater than 1.8v then I would not recommend connecting it to any 96Boards device.