1.) Having his testicles removed isn't cruel, he wont feel a thing, and everybody will be happier in the long run. Using his testicles as an extension of your own is cruel, however, just so you know =)
2.) What's REALLY cruel is bringing more pet quality, unwanted puppies into a world already FULL of pet quality, unwanted puppies. Go to www.petfinder.com and look up Staffordshire (by the way, it's ONE word, no hyphenation, despite what spell checker may tell you!) Bull Terriers in your area, see how many you come up with. I promise the number will shock you.
3.) What's also cruel is the fact that around 90% of these perfectly good pet quality puppies being put to sleep in shelters, come from irresponsible dog owners looking to "calm their dogs sex drives", when dogs, in fact, dogs don't have a sex drive. Dogs don't mate for the sake of mating, they do so for the sake of creating more of themselves, plain and simple. Sex to dogs is not the same as it is to humans. They don't crave or desire sex for pleasure, they do so for procreation purposes.
4.) A dog humping things at random is NOT the dog wanting sex, it's the dog showing dominance over you and other things. Correct the behavior, train your dog, and it wont be a problem. Allowing your dog to breed with another will NOT calm this behavior, and can in fact make it worse, as someone else mentioned before. It will also create yet another litter of pet quality, probably unwanted puppies, that will more then likely end up in a shelter, therefore making the pet overpopulation problem worse.
5.) Should your dog actually be breed worthy, (aka, your dog is show worthy, has show titles, working titles, etc... has had all the correct health and genetic testing done -this does NOT mean a basic vet's clean bill of health- your dog is cleared of any and all health and genetic defects, your dog is as close as possible to the breed standard, and your dog is at least two years of age), and should you be able to find a female that is also breed worthy (aka she meets the same criteria I listed for the male), should you have a stud contract, etc... then you should look for a female in the show ring.
If your dog is breed worthy, and you have him in shows, etc... then it shouldn't be hard to find a correct female for your dog. You should also look around the show ring, etc... for a breed mentor that has been correctly and responsibly breeding your breed of choice, has years of experience, and is willing to guide you through proper and correct breeding methods. If none of the previous listed applies to you, do everyone a HUGE favor, and have your PET neutered, and enjoy him for the PET that he is. Then seek behavior training from a professional trainer or behaviorist, about the humping issue.