@pluggy: didn't the voltage drop when applying a load? It's usual that chargers give out higher voltage without a load present and when reaching nominal current, voltage dropps.
About the diode, if it's on the arduino board, I'd say just leave it there. It's a nice protection against reverse polarity and it doesn't cost you anything. So in my oppinion, it would be the best not to solder your new power suply to arduino but buy a connector that fit's in arduino's power socket. Then you can use this power supply for multiple boards (at least that's what I did and it's quite handy, when having about 5 adruino boards :
)
Regards,
Peter