Chiefs are very fragile. The stegadon is probably the best option, everything else it just too much of a risk for the points you're putting into him.
However, if put a priest on a terradon or give him the cloak of feathers he can fly around and shoot magic missiles via channeling from the slann.
Lore of Beasts would be interesting against O&G, of course this means you'll have to use a slann. The beast cowers against his wolf/spider/boar riders or chariots would be pretty sweet (they can't move or attack). Or, if you could fly the skink priest to the flank of an orc unit and get the hunters spear off (basically a str 6 bolt thrower shot that ignores armor saves) you could lay some major hurt on these guys.
Use skink skirmishers to trigger his fanatics to minimize casualties as well.
As far as hunting goblin shamans goes, he'll probably stick his shaman up in the front of a big goblin unit with an item that gives him dispel dice based on the ranks of the unit. It's going to be hard to get at this guy with a skink chief. However, a cold one rider unit that has been magicked into the flank of the goblin unit could run him down.
I know this has gone WAAY off the skink chief topic, but basically you should win because Lizardmen are so reliable (minus cold one riders) and O&G just aren't.
If you want a good skink character, use a priest. If you want a good fighty character, use a scar vet. Chieftains are only really good for getting a cheap hero or another stegadon.
That is all.
