I've set Chromium to use the GTK+ theme and a custom icon set/oxygen.

However, I've disovered the icons it's using are stored at: /usr/share/icons/gnome/

It uses stop.png, back.png, refresh.png

I want to change the icons and I can overwrite these files in /usr/ but what's the correct way to do this? Where should I place the icons in my home folder it order for it detect and use them correctly?

If you place them in the appropriate directory at ~/.local/share/icons/<theme name>/<theme subdirectory>/ then those icons should override the system-wide theme.