Whether I'm at home or traveling, I shave in the shower. As soon as I am through with the razor, I make sure to place it outside the shower area (top of the toilet tank is usually close by). Two more things will help. If a blow dryer is available, run it across the blades for 30 seconds or so. Then I put the razor in my travel bag near one of those silica gel packs which attract moisture.
I can get at least a week out of most good disposable razors taking those precautions.