I haven't actually hiked Katahdin yet, but did help plan a trip there that got cancelled less than 12 hours before it was supposed to begin (and I was already in Millinocket).
So to answer some of your questions...
There are plenty of options to get to the top of Baxter Peak (the summit commonly known as Katahdin, and the northern terminus of the AT) without traversing the Knife Edge. The most common is to follow the AT itself (the Hunt Trail). Others are the Saddle Trail or the Cathedral Trail. When your books come in just look at the maps and you'll be fine.
The only thing that will keep you off the summit is the weather. Baxter State Park is highly controlled and if the weather (generally wind) is bad enough, they will declare a red day and ascent above treeline will not be permitted. The odds of that are pretty low. However, I would expect cold nights and possibly even snow or ice at the higher elevations. A down jacket is definitely not overkill. I would bring long underwear, wool cap, windblock balaclava ... in fact, since you're staying in the area and day hiking, load up the car with a full variety of clothes.
Other hikes? There are a ton right there in Baxter State Park - peaks such as Hamlin, the Brothers, Fort, Doubletop and Coe. Throughout the park are miles of trails to just walk along; no summits, just beautiful woods.
That's all I've got off the top of my head - others will definitely chime in!
