As said, use strong bleach and water to sterilize your tools between cuts. I use pool chlorine at a pretty strong concentration, but liquid laundry bleach will do fine at a rate of 1:10 bleach to water. O/w you will spread the fireblight youself making the cuts.
Fireblight will also attack pyrocantha and all the pome fruit trees. Your trees are most suseptible to spread during flowering, and bees and other insects will spread the disease very rapidly. Spray with low consentrations of Bordeax or copper when blooming, but you may need to spray them every 4-5 days during blooming to be effective, especially if temps are above 60 degrees F. The spray may affect the fruit by russeting it.
You need to cut the branches farther back than it appears (as a canker) to be infected on the surface. Maybe a foot or two. You can cut the bark lengthwise on an infected branch and peel it open and follow the infection from a canker. It will be brown, red, and then flecking, which are all signs of bacteria infection. Then you will see good wood. Cut at the point a few inches into the good wood.
Water sprouts and fast growing branches are the most suseptible to blight infections. If you have a bad infection, do not use nitrogen in spring and use less water to slow growth of the trees. During warm wet summer weather, the bacteria grow the fastest. Anything growing on the tree that has been exposed at that time will be infected further. I have seen fireblight move through entire orchards in a single year if left unchecked. It is not easy to erradicate, and if your neighbors have plants that are suseptible or that are infected, it can be impossible to erradicate completely.