The 1060 consumes very little power and produces very little waste heat. I don't know about the Zotac cards in particular, but some ITX-sized 960s and AMD 380s are just as performant as dual-fan models of the same card. The smaller heat sink is, however, objectively worse. You'll see slightly higher temperatures (2-5 degrees), but they'll be so far below the maximum operating temp that it's negligible. Really, any cooler longer than the PCB is overkill for something this efficient.
So, is it worse? Yes. Does it matter? probably not. If you're ready for a new GPU, just go for it.
It will negatively affect cooling and as a result it will most likely be noisier and will have less OC headroom. Unless you're limited by space in your case don't go for the mini version(s).
Thanks for the replies. It's definitely something to think about then. A few degrees isn't really a huge deal but noise is something I'm not a fan of (worst pun ever?).
This super limited stock situation with 1060s and 480s is making me antsy lol.