Depending on the weather you could have a decent Knife Edge to walk or a very difficult one. In late July, 2009 a group took part of the route you are describing and shared some very scary stories about being totally socked in on the Knife Edge with high winds and very slippery rock. Plus the descent off Katahdin is no picnic either.
Not to discourage you, but please think about staying safe. A number of SOBOs who started in late July (including some very experienced hikers)spent more than a few days recovering from that first day on Katahdin. Sounds like you are talking maybe near a 30 mile day…the Maine mountains and woods can be demanding and challenging in some very unexpected ways.
BTW, there’s couple of a very nice shelters acros the rd. from the Abol Bridge store (I think it was $7 or $8 for the night) and the river runs right in front - or there’s the campground. If you have a hammock or a smallish tent then there are places on the AT where you could camp off the trail after you cross the bridge.
Good luck with your hike!
singing wind