I think it's pretty safe to say that if you're wearing a kilt anywhere other than a highland games or Burns Night, you are probably going to stand out, regardless of your neckwear. That said, I wear kilts regularly for daywear, almost always with a bow tie.

I also agree that Darcy Clothing is a great resource.

I would tend to picture the "string tie" style more with the sort of "western" suits and cowboy hats popular with country musicians in the 1940s-50s, much like the Southwestern "bolo tie". However, as noted, if you're going for historical looks, there have been a variety of neck-cloths and many different ways of tying. Not all of these will look so keen with a kilt, but most would be an improvement on some modern styles (such as the "rouche" tie) that are often promoted by the kilt rental industry.

Andrew