Don't know about the C600, but you can change the headlight bulbs on the C650 without any tools. With a little effort you can reach up under the front wheel cowling and change the bulbs. You have to do it by touch, but the owner's manual has pictures the show you what to do. After the first time, you can change a bulb in less than 5 minutes.
Your post encouraged me to try so I took up this challenge today after my high beam went out last night. The rubber cover was easy enough to remove but I don't have the manual so I used my iPhone to take video because I couldn't sus what was holding the bulb in. The video worked like a charm and allowed me to see how the retaining clip held the bulb backing and how it functioned. It was relatively simple once I knew what I was working with. (I don't think small hands are required either.) So the first one was 15 minutes. The second one should have been 5 minutes. However, I got too confident and mistakenly took the retaining clip off before removing the socket connector so I struggled a bit to get it off the bulb. Then for some reason I had a bit more struggle getting the retaining clip in the right place for the new bulb. So it was more like 10 minutes or so. But it worked!
I still think it is not too difficult a process so long as you understand whats going on and much better than removing body parts. Here's what I think is gong on:
1. Rubber cap removal
2. Pull off socket connector (remember its orientation which is simple and it will want to go back in the same place)
3. Pinch retaining clip at the bottom to navigate each side out of its holding point. Or you can remove them one at a time. (It's like a horse shoe shape hinged at the top.)
4. Swing the bottom of retaining clip back and up as it is hinged at the top and the bulb will come right out. Note the orientation is the "point" is on top of the back plate. This is how it fits back in correctly.
5. Fit the new bulb in place with the correct orientation. You'll see it comes further in place and fits "snug" and looks "right"
6. Swing down the retaining clip and pinch it together at the base of the bulb to navigate each side of the bottom of the clip into its holding point. I think it may also work doing one side at a time but it make take a bit of fiddling and pushing.
7. Re-attach the wiring socket.
8. Re attach the rubber cap.