I'm surprised you have the problem at all. On most bikes you can flip the back wheel and change the sprocket by a couple of teeth and the wheel will still fit nicely without adjusting the length of the chain. The only thing is to get the brake blocks adjusted so that they catch the rim in either position.
The position of the back wheel is not critical to half an inch when you have horizontal dropouts as your bike does. Looking at the picture I'd say take 2 links out of the chain, move the wheel forward to compensate, and reset your brake blocks accordingly.
However, if you need to make the change, then do it with a single half link. You will derive no benefit from a half link chain except a tiny bit more style, possibly at the expense of weight and price.
The frame will not break under the stress.