I have a situation wherein I need a groove similar to what you want. It's thin, it's shallow, and it is a rare occasion when I need it. I use a cut down hacksaw blade in a small cutoff tool holder. The only stipulation here is that I do not use a hardware store blade, I use a Starrett HSS blade. There is a carbon steel blade by Starrett that I avoid like the plague. The HSS blade is shaped and sharpened just like a lathe tool, i.e. it's kept cool while it's ground.
I will concede the groove doesn't carry any load, the clip is there for a "just in case" application. But it works... ...