How to change thumbnail size without Command + J On my mac (macOS 10.12.6) I can't find a quick way to resize image thumbnails in icon view mode.

I remember many years ago, with Leopard, by using Ctrl + Scroll Up/Down it was possible to resize thumbnails.

Is there any way to use that functionality or third-party software that enables this functionality in Sierra?

I am using a normal keyboard and a normal optical mouse. Not a Magic Keyboard or a Magic Mouse.
I’m assuming you also don’t have a trackpad,  so the easiest option would probably be to make sure you enable the Status Bar in Finder and then you can just use the slider at the bottom right of any Finder window.

To enable the Status Bar, go to View > Show Status Bar.