I am not sure where your controller is getting the idea that voiding an AP check voids the invoice that the check paid because that is not correct. Voiding a check re-activates the voucher. This is true whether you void at the keep check level or after the check is kept using the void check menu item. I wonder if your controller is confusing voiding of a payroll check that, if voided after the check is kept, it does not re-activate the hours.
To answer your question on how to void just one check; if you have not yet kept the checks and are on the check update screen you can use the select handling option and then select which checks to keep, which to void and which to delete. There is a difference between voiding and deleting. Void retains the check number and flags the check as being voided. Delete leaves it as if that check number was never used so that it can be used over again. As an example of how to use these three options, let's assume you were printing a batch of checks and part way through the printing the printer fouls destroying a check in the middle of the batch so you turn off the printer. This leaves you with some good checks that were printed, a destroyed check and some remaining checks that have not been printed on and can be reused. So, you keep the good check numbers, void the destroyed check number and delete the unused checks. You can then do another check run specifying the first unused check number and SL will pick the vouchers for the voided and deleted checks and assign the next check numbers to them.