You might consider having a professional take a crack at sharpening that razor, the result may surprise you. I sharpen my own knives, with enough practice I can put a keen edge on a kitchen knife or pocketknife, but putting a razor's edge on a straight razor is about as difficult as sharpening gets, I'm fairly sure I wouldn't do as good a job at that as a professional would. You'll want someone who specifically sharpens straight razors.
I specifically sharpen straight razors! (Or I used to - I'm a beardie-weirdie now). I'm not up to grinding out a nick, but I have a coticule and I can use it. I used to know a barber who could do a good job of razor-repair.
You're right, sharpening kitchen knives is much easier.
