You definately don't want to use a razor!
You don't shave down to the bare skin when you do it.
I would shave them and give them a day or so to see if they come back up...I have a girl now nearly a year old with ears that will start to flop if the hair gets too long, but they are back up when I shave them.
I have some clippers (ConAir I think) that are small, beard trimmers. I think they were only about $10 at Wal-Mart. They work great!
