There isn't a single club in Europe which will pay twice Damsgaard's transfer fee for Shaqiri, this summer.
One is a talented youngster who looked impressive technically, clever, and looks like a fit for a top club. Shaqiri is also very good technically but his age, injuries, journeyman career, never really established himself at a top club, we are also looking to get rid to raise money means that we won't get more than 15-20 million for him at max.
I was very impressed by Damsgaard but I am not saying we should buy Damsgaard at 34 million. I haven't watched him enough. Your argument against him was his stats. Then you put Julian Brandt as an alternative whose stats are equally bad. Brandt is 25/26 and close to his peak. Playing for a team and in a league where attacking players shine and put up impressive numbers. I would definitely prefer Damsgaard over Brandt.