Are the male and female genitalia "the same" in every respect aside from their shape?

All men with normal male nipples have milk glands that would produce milk.
Making that happen generally requires external hormones. If you started taking female birth control pills, you might lactate.

OK, but would it affect any other secondary sexual characteristics?
Reduce my body hair, make my beard sparse, give me thicker subcutaneous fat layer, less muscle mass, change the odor of my sweat?

If you took external hormones in doses that produced lactation, you probably would experience other effects as well.
Everyone is different, every body is different. So a specific answer is a bit difficult.

As an exercise in applied endocrinology, it would be fascinating.
Feed a male friend just enough of the right chems- without him knowing- so he leaks milk.

Then put 'em on ebay.

Its been a half an hour and I’m still laughing over this! :smiley: