Squirel, I'm not sure you can buy a stronger H2O2 (except if you are an industry). 30% (130 vol) is what is available in hardware stores. I believe 35% does exist, but have never seen it.
with it, you are adding water to the wood, no wonder it moves if the wood is not stable. it will also raise the fibers a bit. Like John, I have never put anything to neutralize the bleach before applying a finish (oil). but most of the time bleach is followed by other steps before the finish.
Gretch, I never wondered about green or dry wood. for sure I've used it on both and haven't noticed a difference. there's no risk in trying. the walnut or danish oil will add a yellow tint to the wood. the best finish is no finish.
all this is experimentation, I've developped my method with various comparative trials over the years, on the woods I use. the best advice I can give is "try, and let us know the results".
Pascal