Becks has said in the past he'd like to try a more central role in midfield. Why not put him there and move Chadwick out to the right wing, since he'd be better out there than in central mid.
I wonder whether the replacement of Cole and Yorke with van Nistelrooy and Solksjaer (or RVN alone) hasn't diminished the effectiveness of Beckham's crosses. He likes to hit them diagonally from deep - ideal for Cole's pace to run on to - but which doesn't suit RVN or Solksjaer (neither of whom have either pace or are an aerial threat). I think these two would be much happier with crosses pulled back from the goal-line - not something Beckham does very often. Whether Chadwick is good enough for a regular start to do this I'm not convinced as yet.
At the time of the question, all four of those players were listed as injured. That left Phil Neville as our central midfielder. Wouldn't you rather try Becks there instead?
Giggs doesn't cross the ball well either. He runs at defenders and sends low square balls to the middle which suits RVN and Ole much better (as was pointed out in another post). Chadwick is more similar to Giggs than Beckham is, and it's not like Becks wouldn't float out to the wing and send some balls in too....