Soft is bad when it comes to driftwood, especially when the whole piece is soft. Hard wood works best, it won't rot and break down as quickly.
Is any portion of this driftwood solid? I've had pieces where there are some pockets of softness. I just soaked the wood and scraped with a wire brush until I removed the soft parts. The remaining wood was very solid and didn't break down.
As for making the wood aquarium ready, use heat. Boiling is good. It not only kills any nasties hiding in the wood, but it also helps rid the wood of air pockets encouraging it to sink. You can also bake the wood in the oven to kill nasties. I have no experience with that method however.