What you have there is a Female Cooper's Hawk, (Accipiter Cooperii), not a buteo (buzzard) but an accipiter, or "shortwing" in falconry terms. She looks to be of passage age.
Capable of short lasting great bursts of speed, primarily a bird eater. >>I<< call them "North American FACE CATCHERS". I have had several, they are fun to fly, but when they are on a kill, they mantle the kill as if insane, then, without warning, turn, fly into your face and rake their talons across your mouth, nose and eyes. I;ve often called them "Guided missiles with wings".
You are fortunate to have only had your finger punctured by her talons as a coops can go absolutely NUTS without warning. Had THAT been a Goshawk, she would have REALLY given you a good "honk" with those feet as they have tremendous crush strength. Even the coops can give you quite a squeeze and armed with those talons, anything short of a thick falconry glove will easily be pierced. Imagine a buteo such as a red-tail (Broad wings) on your fist! I actually had one of those puncture through a triple ply elk skin glove into the first knuckle of my index finger. Caution when catching raptors, a broken feather or two can make the difference between catching wild game and starving as the moult does not begin until late spring and lasts through until October where they replace old plumage.
If you have a love for raptors, IM me your email addy and I'll send you some pix of the various hawks I've kept over the years. I've had some great coops, I have had even more 'tails (Red-tails) and Hariss Hawks as I am more of a "Dirt hawker" and they are great "Bunny busters and I have slaughtered some insane headcounts of jacks with the broad wings. (Razorblades with feathers)
If you REALLY like raptors and are interested in flying them on wild game, consider apprenticing under a general or master falconer (I am the later), look up your state's F&G for your state's apprenticeship program and a referral to the state falconry club or NAFA for referral. Apprenticeship is two years before being released and signed off to General Falconer 1. Also, get a copy of "North American Falconry and Hunting Hawks" by Frank bebee & Hal Webster and "The Falconer's Apprentice" by William C. Oakes. Get a sponsor and then your apprentice license and using a bal chatri, trap your first passage red-tail for use in hunting, "sky fishing" is a blast! And you won't even have to use your shirt to catch the hawk!
The state and federal licensing process is exhaustive but by no means "hard". There's a required written exam, a facilities and equipment inpection, a minor background check, F&G warden will then sign your application inspection block, your sponsor will sign his/her block and you pay yoru fees to the state and fed and wait 3 to 6 weeks (Typically two weeks) and your license arrives. Hoodmaking is fun too as well as making your own jesses, anklets, leashes and various perches. I warn you, it is an OBCESSION and a blood sport and a hole to throw $$$ down, especially when you buy kangaroo leather for your home made equipment and hoods.
OOPS! Look! I wrote another BOOK!. *wince* I'll shut up now...