2oz will be very thin, especially for anything large than a card wallet. It can work, but if you don't want it to distort & stretch & lose its shape, I'd recommend a thin lining, which won't add much thickness. Even without lining, you can add shape stability but stitching the single layer around the edges. The stitching will prevent more severe shape distortion.

Even if you decide you need thicker, 2oz can be a good side to start with, because you can always cement two layers back to back, basically using the 2oz as lining itself. This way if you're just getting started, you don't have to worry about buying multiple weights or trying to thin down a thicker weight, etc.

As for other animal types, horse leather, usually sold as horse-fronts, is thinner, usually 1.5 to 3oz, and often a bit tougher for its thickness. I'm not sure I can recall a readily available veg tan option for it, but Maverick usually has a variety of options. You can check their website to see, but phone orders are all they accept. I'd recommend that anyway, since they'ye great to work with, always helpful, and can answer questions about their stock such as whether the horse front you're interested in is firm, or tumbled & floppy.

If push comes to shove, I have a bit of firmer horween horsefront, sourced from Maverick, in a tan color, and I could part with a square foot or two.