I got the 1st Recon Beret from Boone, but while I love the stats, I hate the way it looks on my character. How would I go about editing it in the GECK so that it looks like I'm not wearing a hat when I put it on? I tried deleting the model & texture from the Biped Model entry for the item, but that made my game crash when I tried to load my saved game.

Any suggestions on how I would go about this?

Hmmm, the only thing that comes to mind is making a texture set for the hat, and pointing it to a texture that's entirely clear. That would load a clear texture onto the hat, effectively making it invisible.