Your patients are probably confused. Certain screenings (such as mammograms) are provided without a co-payment by the insurer (and here in Florida, that's state law), but I am not aware of any payer or state that includes skin cancer screenings among these.
Although V76.43 is the correct code for skin screening for malignancies, we never use this as a primary diagnosis, because it is not payable by insurance. We do as you do; bill the diagnosis based on the findings and, if there are none, we use V10.83 or V10.82 (personal history of skin cancer), which are payable. I don't think we've come across a patient yet who didn't have one or the other (findings or history)!
I would explain to the patients that their insurance does not even cover skin cancer screenings, much less waive the co-pay, so if you billed it as a screening they would have to pay for the visit as a non-covered service.