Those tap extractors will work, as long as the tap is in one piece. If it is cracked, and parts are still in the hole, you will need to try and pick out the broken piece. If you don't get out broken fragments, it will bind in the hole, and possibly break a flute on the extractor. Also, it's a lot like tapping a hole. You need to turn it, out a little, then blow out the shavings, then turn it back in, until it turns freely. When you're tapping a hole, by hand, turn the tap a little bit, then back it out, clean out the chips, clean the tap, add some more oil, go a couple treads, then repeat the process. If you attempt to tap a hole, all at once, you're asking for trouble. Machine tapping can do it, but they are usually flooded, with coolant and working with a straight hole and tap is aligned better. Not so by hand.