I don't understand how the teams are as they are.
In a 64 team competition, we would have 32 teams left after round one. For whatever reason we have 38.
After round 2 there should be 16 left, we will have 19. The numbers always have to be a even to achieve a 64/32/16/4/2 tournament. When we finish this round we will have 19 teams in a field that should be 16 so I'm not sure how there will be byes. If you are saying that we will have an odd number of teams that is right but if we have more than 15, then the bye doesn't work.
You can't give both teams a bye into the next round if they didn't play. That creates chaos in the numbers and makes it impossible to achieve the proper brackets. One team should win or both should forfeit, there should be no both advancing, that isn't far to the teams who played and won or those who played and lost.