You are correct that the timing of progesterone only pills is important.
Dr. Deena Zimmerman, medical director of our website, recommends gradually adjusting the timing of the pills. If you currently take a pill each morning, you can gradually alter the time in advance, moving about one hour later each day until you are taking a pill in the evening. After the fast, you can gradually move the time back to the morning whenever it is convenient. Since the change in routine may make it more difficult for you to remember to take the pill, you may want to set up some type of reminder (e.g., on your cellphone).
If you cannot adjust the timing, and if this pill is neither sugar coated nor sweet, you may swallow it directly without water. As it is a small pill, water should not be necessary. If the pill is sugar coated or sweet, you should wrap it in a kosher gelatin capsule (available at pharmacies), or in a small piece of paper, before swallowing it on Yom Kippur morning without water.
G’mar chatimah tovah!