You are right, I noticed the big white shoes as well but quickly forgot about it after the movie ended.
If you look closely you'll see how his shoes are just too long.
Here is a screenshot of that scene:
Just before the scene David tells "Mother" to play Richard Wagner's "Das Rheingold" - the plot of the drama is about a dwarf who steals some magic gold. He forges a powerful ring which will enable its bearer to rule the world (but he has to renounce love to do so).
(Read the Wikipedia article for the full story: https://en.wikipedia.org/wiki/Das_Rheingold#Scene_1)
David basically does the same thing, there are many similarities between David and the dwarf of that story and my guess is, that Ridley Scott just wanted to give a (hidden) hint: David with big shoes looks like a dwarf - and he is now the one who stole something and "forges" something very powerful.