just what you told us here.

 
They just may appreciate your candor and work with you, or they may suggest a non-refundable fee (25%?) as a hedge against their losing income owing to your needs.

 
In any case, to go ahead and cancel last minute with no warning is probably the worst outcome as you'll find yourself on DNS lists before long.

Dont book the ones that have policies you dont feel comfortable with. Otherwise, be open and honest, let them know the second you realize you cant see them, and ask them what they request as part of the cancellation, if her policy is not listed on her site/ad. If it's payment in full, so be it. Sometimes the lady will offer a number between full price and nothing. Being a gentleman means following what they ask to the letter, especially since you were the one that cancelled last minute in your hypothetical.

Assuming you can commit to a narrow time window (a few hours) w/o a last minute emergency, I would hope that you could find a hostess who would agree to meet on short notice IF her schedule can accommodate you.  
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Describe your situation; let her screen you in advance; let her fill her schedule with more definitive appointments. If YOU "suddenly" know with certainty that you have time on a day she's working, let's say, one hour between 2PM and 6PM (w/o being sidelined), contact her ASAP (9AM? 11AM?) and hope that she can fit you in (yeah, yeah, double entendre intended). Maybe she had a cancellation. Maybe she never filled that slot at all.  
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Once she knows your situation and AGREES to see you on short notice, when possible, don't pester her. On the day of, (a) remind her that you're the pre-screened short notice guy and (b) ask if she can see you in your time window. Don't expect an immediate reply (or any reply at all) to your email, text, or voice message. She might be in a multi-hour meeting or otherwise occupied. Let it go and wait for the next time your schedules coincide.

much of what's been said here.

 
Be upfront.  I always have a bit of risk in my schedule.  I try to schedule at least a week in advance, knowing that my availability may change.  I let the ladies know that up front.

 
Be familiar with the cancellation policy.  Some providers will be understanding.  Some will insist on a penalty right up front.  And some girls will blacklist you, until you reschedule within a certain period of time  (e.g. if you don't reschedule within 30 days, they will not accept future date requests).  Decide which ladies you want to see based on your tolerance of their policies.

this comes down to a question of "habitual" versus "occasional."  10% cancellation rate is not bad if you are seeing the same lady regularly, but for a specific lady, there is a good chance you booked once and cancelled once, or booked twice and cancelled once.  This puts your cancellation rate in the 50-100% range, and I don't know any providers that would be okay with that and want to continue to see you.    

 
In the past three years, I have had about 350 sessions with providers and I only cancelled same-day twice, once for a car accident I was involved in on my way to the session, and once because my aged father was rushed to the hospital.  Otherwise, if I think there is any chance I will not make it, I don't book.  

 
Your own reputation for dependability when you book can make or break your hobby life.    If you are cancelling the same day with a lady you are seeing for the first time, you should offer to pay anyway.  You should not wait for her to "demand" it.  The cancellation is on you, not her.  Do this a few times and it may make you more circumspect about how you approach booking.  On the other hand, you might eventually be blacklisted with just about everyone and the problem will fix itself.  Lol

There may be more going on than you care to share about the new state of life for you. However, I would think things like kid getting sick once they've gotten up and are not sick should reduce the chance of that emergency from the 10% to something a lot smaller. Maybe the same is true for many/all of the other sources of emergency. If so then same day booking seems where you have to go. Perhaps there is also times of day that will also minimize the incident of some need to cancel so when you schedule could be a facto here.

 
As was noted, if you're dealing with some regulars then 10% is not really a big deal and they should understand if you need to cancel. If you're more the one and done type you might consider finding some favorites to see one some level of regularity (how often do you see someone?)  which might at least prevent the worst case worry of getting on some BL and not having anyone go to bat for you from the provider side.

Just have certain days and times on your schedule, I think that would help quite a bit.
If you think about certain scenarios try to put together backups for those things.
Hopefully, that can cover most things.
The other stuff, hospitals, bigger accidents, jail cannot be helped.
So, stay healthy, drive slow and safe and don't talk back^^!