You don't need a ball nose to produce this type of project I work in stone, metal and woods cutting relief carvings and use V cutters or engraving cutters between 90 degree and 10 degree with a 0.020 truncation ( slight relief off point).
I would run a roughing pass with either a 4 or 6 mm ball nose leaving 1mm of material to finish pass with the engraving cutter and you will be fine you should have no broken cutters.
Don't forget if you have any deep, steep sides in the relief you need to use a smaller angle cutter for the finish pass this is why I go down to 10 degree inclusive angle, if you intend to cut a lot set yourself up with a cutter grinder you can regrind to suite your project then.

Phill