I'm pretty sure it's fine. (I use Mach 3 too)

I do carry my razor on long haul trips, especially if there is a transit (like SYD-JFK via LAX) because I like to keep fresh and neat. I put it in my amenity bag that I bring with me. I always detatch the blade from the stick... I just tend to think it would look less offensive on the x-ray. Am I a little odd?

Just be careful with cans of shaving gel or foam. I bring only the small size if I have to bring one at all. Luckily you will get some cream or foam in most J/F amenity kits. Thank you QF for that!! ^ I save these where I can for trips where I don't expect to be given one.

(this goes for hairspray too. They will seize any oversize cans. I once packed a mega big can of hairspray in my carry on by mistake! Bye Bye! And no this wasn't in the 60's for a beehive doo!)