Newbie pocket milling question

Mind a question from a newbie?

I've had this problem in some form or another on almost everything
I've made -

I'm trying to cut some walls for a model RR station. It's spanish
mission style, with windows in those arched bay thingies.

My software (Modela Player) does a "draft" cut, then a fine cut.

To get the surface detail (stuff like muntins on windows) I need
to use a small dia. cutter. I'm using a 1/32" cutter.

but the detail extends up to the edges of the bays. The stupid cutters,
however, only have about 1/16" of flute (reasonable), but then immediately
taper out to the 1/8" dia. shaft. This conical transision is ruining all
my cuts!

I'm cutting wax, and some styrene.

Anybody have a solution to this problem?

Annie