Your gut reaction to hearing your baby cry is telling you that it isn't natural to hear your baby cry and not go to them and comfort them. Your body, as a mother and parent, is designed to feel that way so that you will respond quickly to your baby. This is natural and is telling you not to let him cry, but to be there close for him :-)
Why does your 1 year old need to learn to sleep on their own right now? Is this something a well-intentioned friend or another old-fashioned parent or Dr. has led you to believe? I always find it odd that we don't expect our babies to be potty trained or speak clearly by such a young age, but in America there is this crazy expectation that little ones are supposed to have or develop a higher learning sense of independence already. Babies should learn to rely on other people especially their parents when they need them. This creates a strong sense of security, love and trust that will carry far into life.
You mention that you know he isn't hungry or in need of a diaper change, but what about a 1 yr olds need for comfort, closeness, security? Many children need this day AND NIGHT for much longer than 1 year. This is as important, if not MORE important than needing food or a fresh diaper. With children going through soooo many changes, developments, teething, growth spurts, growing pains, emotional changes, etc you can never possibly know all the times that they really need you. To not respond just because they are full and dry would mean they are also not getting their emotional and mental needs answered also.... The Ferber method is highly controversial, and I don't recommend it, especially for a parent that has done so much good already for her baby by rocking and being close for so long. You have done so well! I would recommend a Dr. Sears book..either Nightime Parenting or Attachment Parenting for you and I think it will suit you and your husbands desires for reaching a little change in the gentle-est of ways. It will be less stressful and happier for you both as well as your oor little guy :-)
Be there for him, day and night, not only for his physical needs, but those of mental and emotional as well. If you could ask him, he would say he wants to be rocked and held, and wants you close. He doesn't want (or need!) to cry himself to sleep...how sad, and I don't think you want that either :-)
Keep him close while he's young, it goes so fast...best wishes!