DD does a bit of this too.... I give her the pack of baby wipes to hold and she's happy (most of the time it works!!) she loves the crinkling sound the packet makes and she thinks she's helping me by taking the wipes out!! Cute.
Like the girls said, distraction is the best!!
And I also talk to DD and say "it's ok, I know you are upset and angry but I won't be long I just have to change your nappy and then you can play ok??" just talk to her.