Hi, DJ. If the relationship is through your father and your aunt, it sounds like the new match would be a 1st cousin 1x removed.
Following the instructions about WikiTree DNA use and confirmations, per WikiTree policy you can certainly mark your father as "confirmed with DNA." That said, your cousin must have a profile on WikiTree (with his DNA test information entered), and all the profiles connecting the two of you--including your father and both grandparents, and his mother and his grandmother (your father's sister)--also have to be in place.
Following the instructions I linked to, and making certain each profile has the appropriate DNA source citation, you'd be able to mark your father as confirmed, and he would be able to mark his mother and his grandmother as confirmed. In other words, each step up to but not including the MRCA couple, your grandparents. Of course, that's assuming I've got the 1C1R relationship correct....