In 1/350, a chisel edge X-acto blade should do the trick, or even a single-edge razor blade, if you take your time and just scrape away a little at a time. One thing, I would mask the detail around each stair, especially any plank detail on the deck, to avoid inadvertently removing too much of what you want to keep.
IF you think you are going to be doing a lot of ship models in the future, virtually all of the ship kits have these Aztec stairs. I build in 1/700 and prefer a chisel. Quick, clean, and a few cuts gets the job done. I got mine from Micro Mark: http://www.micromark.com/2mm-Plastic-Modelers-Chisel,8175.html. It may seem pricey but it sure saves a lot of time!