Welcome to our Forum I'll be glad to comment and provide some more general information. There was no risk whatsoever from the event you describe. STIs, including HIV are not transmitted to others through masturbation. this is true even when partners get each others genital secretions on one another during mutual masturbation end no matter whether either or both partners have scrapes, cuts or sores on their hands. Still no risk at all. There has NEVER been a case of HIV transmitted through masturbation- penetrative sexual contact is required to transmit HIV.
In addition, I will point out that most masseuses do not have HIV, nor do most commercial sex workers and exotic dancers. With this background, I'll address your specific questions.
1). If the lady had a cut on her hand and then gave me a handjob would that transmit the hiv.
No, still no risk.
2). Should I take PrEP medication since the exposure is less than 72 hours? Does it have any side effects.
There is absolutely no reason for you to take PEP (not PrEP since that is an acronym for Pre-exposure Prophylaxis) because of this event. If I were seeing you as a patient and you asked for PEP under these circumstances, I would refuse to do so. I should add that both PrEP and PEP are rather expensive and do have some side effects (mostly GI upset)
3). Will I be able to get PrEP medication on walk-in basis or appointment is a must. I live in Seattle.
See above. You do not need PEP. If you wish to be seen by a knowledgeable clinician, I would suggest you go to the Seattle-King County STD Clinic at Harborview Medical Center (I used to work there, Dr. Handsfield still does), which is one of the world's best and most progressive STD Clinics.
4). I am worried if I keep wife at risk if I have sex.
Your wife is not at risk, there is nothing to worry about. There is no reason related to the episode you describe to abstain from unprotected sex with your wife.
I hope these comments are helpful. Please don't worry. there is no risk associated with the episode you have described and no need for testing of any sort. EWH