Dying hair after FUE. Is natural hair dye any better than "Just for Men?"

[jonesvery]

I recently had a 1500 graft FUE procedure. From what I read, it is advisable to wait 4 week until resuming my hair coloring routine. I was just thinking that using a natural hair dye, free from chemicals, may be a better, more gentle option now that I have transplanted hair (and want to keep as much of my existing hair as possible). So Just for Men vs. a natural hair dye. Does it make a difference? Has anyone had experience with a natural hair dye?