I’ve not read the books. But here’s a thought.
So Tyrion is right clever yeah.
If Jamie is his champion, which is possible ‘cause Jamie is the only one who does care for Tyrion, Bronn has trained him up so he’d beat whoever Cersei’s champion is. Also Tywin can’t let Jamie die cause that’d mean no heir! Also Cersei wouldn’t want Jamie dead. So Jamie would beat Cersei’s champion meaning Tyrion goes free.
If Jamie was Cersei’s champion, Bronn would be Tyrion’s. Bronn trained Jamie and knows his weakness, but again Tywin wouldn’t let Jamie lose. But Jamie doesn’t want Tyrion dead, so wouldn’t want to beat Bronn. So Jamie would be rather torn! His life or Tyrion’s.
But, it is George R.R. Martin, so for all I know, they could all end up dead. They are planning two more weddings after all.