Socket size to loosen rear wheel nut?

32mm. And in case it helps, 1/6th of a turn of the adjusting bolts tightens the chain about 10mm. If you mark where the nut is now with a permanent marker, you can back out both exactly the same amount, and keep the rear axle aligned. That's what I did. A few more tips:
1. Don't use too much force to measure slack. It's better to leave it a bit loose than too tight.
2. Do the right side first, so you don't add extra tension to the chain. Not a big deal, but it's better that way .
3. Don't rely on the rear stand spec (25-35). Checked yesterday, and it's not consistent. It showed 40 before adjustment (or +8), but only 23 after (or +1). Put it on the side stand, and it was in spec at 22. Just checked it now again, and it's 22, so will leave it there. Ideally I'd like it at 25 (right in the middle of 20-30), but it's not worth dicking with the adjustment back and forth IMO, especially when new; it'll keep loosening quicker than normal anyway, so better to adjust it at the lower end. From now on, will do exactly what I just did: wait until it's at the upper limit (or past a little), and adjust it 1/6th of a turn, which will put it at the lower end again, and call it a day.

Finally, I personally think the factory torque spec for the nut is, well, nuts (ha ha). So I use 100, which is still more than any other bike I've owned... and they didn't have a locknut. I still need to use a breaker bar to loosen it. Anyway, just mentioned it, in case you wonder about that too, so you know you're not the only one . Hope this helps, brother.

Yes inddeed you are so right about the torque specs. The manual is very wrong. It cost me 80bucks total with shipping for a new wheel axle and locknut. Threads got messed up. When i get the new one i will use only 100ft lbs.