I now it says it in the book but I can't remember what kind of cologne it was?
I can't exactly remember what cologne it was or if it was mentioned but here's a part I found in my twilight book which gives description: "It was cold —the way my jacket felt when I first picked it up in the morning, hanging in the drafty hallway. I shivered again. It smelled amazing. I inhaled,trying to identify the delicious scent. It didn't smell like cologne." It also states that Bella thinks he smells sweet like honey and lilacs.
dude he's a vamp he already smells nice so he doesn't need to wear anthing