You don't need a particular style to beat Khan. The man was garbage. Bradley would get inside and maul him.
Bradley would have some issues on the outside, but he was effective at getting low and making himself a smaller target, and I think he would close the gap. Khan is far from a ring general, and he gets flustered rather easily for a world class fighter. Bradley wins a decision.
For all his faults and delusions, Khan did hit a good patch of form between 2009 and 2011 and for a while was starting to look like a very capable fighter on the world stage (briefly revived when he breezed past Alexander a few years later). I don't think Bradley has it all his own way. That said, I would still pick Bradley here. I thought Khan beat Peterson and was pretty unlucky with the verdict, but I also think that fight is instructional as to how Bradley wins this - he'd probably make it more decisive than Peterson (he was better, after all) and put it beyond doubt. Too robust, tough and sharp inside for Khan to deal with over twelve. I think it's close for six or seven rounds before Khan begins to tire and Bradley works him over. Don't think he gets Khan out of there, but I see Khan looking quite beaten up towards the end and hanging on. Bradley by 2-3 rounds.