Richard, your razor should be safe in your cabin if your on a major cruise line. Most cruise lines have digital safes in the cabin where you can lock the razor when not using it. I would suggest that you pack all valuables, RX, travel documents toiletries in your carry on bag. I'd also suggest a change of underwear in your carry on and swim trunks. Your bags may not get to your cabin until later in the day and rarely lost, so keep what you can not live without in your carry on.
I use the Gellette Mach 3 razor blades, they work great with shave cream or Pantene hair conditioner works great as a shave cream.