You answered your own question. If they don't meet any of the criteria that some psychologists use to diagnose a personality disorder then they don't have a personality disorder. If they don't have a personality disorder then they are just human. Then again, people with "so called" personality disorders are just human too.
And that is the answer to your hypothetical. People are just people, with and without consciences. What psychologists say or don't say is ultimately irrelevant until you decide to make it so by believing their words are gospel. Normal isn't a real state of being. It's in the eye of the beholder.
But I'd like to know if it happens often - because EVERY time I'm reading about a lack of conscience, it's ONLY about psychopaths and I was curious if there are any ordinary folks who share only this one feature with them. I never before heard about someone with no conscience but not showing any other psychopathic traits.
A psychological "disorder" is not really analogous to a physical disorder, although the use of the same word, "disorder," confuses this issue. A physical disorder has certain fixed symptoms which can be discovered by means of blood tests, MRIs, etc. For example, you either have measles or not, and a blood test will determine that fact. A psychological disorder, on the other hand, normally has no absolute parameters which can be determined by testing, but is a matter of definition and opinion.
If a patient presents to two different physicians with, for example, a high fever and headaches, and one physician diagnoses dengue fever, and another malaria, simple tests can determine which is correct. However, if a patient presents to two different psychologists with an overwhelming need for constant attention, one psychologist could see this as a feature of narcissisic personality disorder, while another sees histrionic personality disorder, and the so-called "differential diagnosis"(deciding which) will be a matter more of interpretation than of fact, particularly since the criteria set for both of those so-called "disorders" was created as a matter of opinion and definition to begin with, and will be changed and modified as time goes on, perhaps even disappearing from the list of "disorders," as homosexuality has.
As I have written often, I consider a lack of conscience--which in many ways really means a lack of the need to conform to cultural definitions of so-called "right and wrong"--to be a normal human personailty variant. I have much evidence for this view which I will not adduce here. Psychopath is simply a label which is used to indicate a certain set of personality and behavioral features--and not everyone agrees what these are. Given this disagreement and the arbitrary nature of the definition, it is more useful in my view to dispense with the diagnosis, and simply deal with the factual situation. For example, I am currently seeing a person who is completely self-centered, cares not one whit for anyone besides herself, uses sex or whatever else she can command in order to manipulate others, and has caused lots of harm to lots of people in her short life. Frankly, I don't care if she is a narcissist or a sociopath--for me, the treatment is the same: listen, understand, and communicate my understanding to her.
I hope this helps.