I would only pink edges on something that was very tightly woven and was very dressy. Pinking frays. I'm trying to think if I've seen any pinked wools in this period, and drawing a blank. And yours is cotton? I would definitely not pink.
My machine has a narrow-hemming foot that does a pretty good job on this kind of thing. I wouldn't use it for the edge of a white collar or anything like that, but for straight strips of trim with a pattern to them it's the bee's knees.
Another period way to approach this kind of trim is to make a sort of flattened bias tube. I say "a sort" of tube because it's not like a modern stitch-right-sides-together-and-turn kind of tube. You cut a bias strip a little more than twice as wide as your finished trim. Press under a narrow allowance on one edge, then lay it right side down, fold the raw edge in just past the middle, fold the pressed-under edge over the raw edge to hide it, press the whole thing flat, and slip-stitch the p ressed-under edge over the raw edge. That is now the underside of your trim.
This trim looks to have been done that way:https://www.pinterest.com/pin/394768723566231771/