Is it OK to use normal spray-on degreaser to clean separated case halves? Or would it harm the machined surfaces?

all good.

As recommended by tazzie super vee, Mr muscle oven cleaner is good to make it nice and shiny.

I use a caustic acid based cleaner and it cleans the case up like brand new. removes all oil stains on everything. i pump it through all the oil galleries and it strips all the sludge and deposits out of them. all other engine parts are degreased then cleaned with this cleaner as it removes the oil stain than degraser won't.