Hmmmm, according to PETA, most of the worlds leather comes from India and China. Their stats say that over a billion animals are killed for their skins every year, and they estimate 2 million of that is dogs and cats.
I guess I would have to avoid leather entirely in order to not get 'dog' leather, which is rather unreasonable. The odds of getting dog leather in this case are pretty slim with those numbers. The vast majority of those 1 billion animals are cows (I'm assuming) which provide a lot more surface area than a dog would. Lets say a cow provides as much as 20 times that of a dog.
Lets say 700,000,000 (70%) of leather is cow leather. If there's 20x the surface area (rough estimate), then there would be 14,000,000,000 units of cow leather out there
Let's say 298,000,000 (29.8%) of the rest of the leather comes from a pig. Pigs probably have 5x the surface area of a dog, so consider that to be 1,490,000,000 units of pig leather
And dogs and cats make up an estimate 2,000,000 units
The chances of getting dog/cat leather are therefore 2,000,000/15,490,000,000
Or 1/7745
or 0.01291%
Chance is small. I'm sure we're probably not getting a lot of it if any, watch straps and all...
Of course these numbers are estimates so the odds could be lower (or higher).
http://www.peta.org/issues/animals-used-for-clothing/leather-industry/global-leather-trade/