I don't think so but there's a hardware button that cycles through whichever ANC options you choose.

Agreed.  You have hardware buttons to switch between the two options that works smoothly.  You can actually switch between ANC, Aware Mode, and off, but you change it so that one of the modes isn’t an option for the hardware button, if you never use Aware mode for example.

I’ve honestly never felt the need to switch modes when changing sources to be honest. I pretty much stay in ANC all the time.

ANC sounds a bit unnatural to me when using over ear headphones when taking a call, as I can’t hear my own voice in the same way as talking using phone handset.

That’s true.  I notice this at first, but have gotten used to it.  Worth noting though that the ear cups do a lo of physical noise cancellation, so even with ANC off, you you are not going to hear yourself as normal.