Yes, BBT-22 & CWP-7 are what I use with square taper cranks/BB. The small "button" included w/CWP7 is for removing square taper cranks; the large "button" included is for removing splined (e.g., Octalink) cranks.

Hint: When removing the crank arms, be sure to fully thread the extractor before attempting to remove the crank arm. You want as much thread engaged as possible. Only partially engaging the extractor is more likely to result in stripping out the threads of the crank arm. On that note, you might take a moment to ensure the threads are clean of any debris that may obstruct the tool. I also use a little grease on the threads.

As you begin to remove the crank arm, you will likely notice some sudden, increasing resistance. This is normal, as the tool is disengaging the press-fit interface of the crank arm to the spindle.

When you reinstall the crank, make sure interfaces are clean and use proper torque. I use a torque wrench, since it's common for ST cranks to be installed with insufficient torque...and this leads to trouble. I tighten sufficiently and then leave them alone. Opinions on whether to lubricate the spindle interface or leave it dry are divided.