Jsfat

Being careful is the first line of business. Working from the bottom will get you wet, working from the top can be dangerous. When the pipe is opened up and the water starts to flow it will scare you if you have not seen it before.
A ten foot stick is a good idea but not enough. Something longer, a piece of 1 inch pvc pipe will help locate the blockage and be light enough to handle. They come in 20 foot lengths and you can add a second or third joint if needed.
A pipe that is full of almost anything it can be worked out with a little elbow grease especially if there is the weight of the water helping push. Just a little hole will often get the mess moving.
You said rusty pipe so I guess it is metal. If it was installed fifty years ago it will more than likely be gone. They can be left in place and filled with concrete, but you may end up removing the whole thing anyway, if so that will eliminate the worry about the blockage.
Otto