Congrats on being cancer-free! That's the best news!
You are correct: dysplastic nevi, or atypical moles, may - or may not - develop into melanoma. I had two removed simply because they developed suddenly post-melanoma.
Having moles removed can be a very personal decision. I had 3 removed because I chose to not keep track of any changes. Another person might not have made the same decision. Your decisions are equally personal, and I can understand that. My concern is for people who get afraid and have unnecessary procedures performed.
It sounds to me as if you might have a fair amount of moles, and if that's the case, you should probably take precautions with your skin. If your skin is fair, if you are blond or red haired, if you've exposed your skin to the sun quite a bit in the past, these are all potential risk factors. (Not that you WILL develop skin cancer) This means being smarter about being in the sun: sunscreen/sun block, hats, sunglasses, etc. Going in for an annual skin check with a dermatologist is something everyone who is at potential risk should do. It's as much a good practice as a physical exam. However, most skin cancer is found by the individual, so that means you should do regular skin checks. It's not that difficult, and really, you are the best judge of what looks odd or different on your body. And, of course, if a mole should EVER change in size, shape, or color or itch or bleed you should immediately have it checked.
Other than this, I wouldn't give it much thought. (I know, it seems overwhelming, but stuff like sun safety becomes second nature after a while) There are thousands of individuals walking around with atypical moles in this world who will never develop skin cancer. Be aware, don't be consumed.