Just got a PS4 Pro, is it possible to just swap the hard drive with our old PS4 to transfer saves?

Title basically.

I've tried googling, but can't find the answer to this question anywhere. only how to upgrade hard drive.

My worry is the PS4 Pro operating system might be slightly different, I plug in old hard drive, and either Pro won't work or saved data becomes corrupted.

I'm aware this is potentially a very stupid question, but any help is appreciated!

Thanks.