If I knit or crocheted something with two strands held together, I would do the same for the border, unless I was working a small attached i-cord edge. An i-cord edge is very unobtrusive, barely noticeable by its size and presence unless you work it in an outrageous contrasting color.
The single strand attached i-cord uses very little yarn. It uses two dpn's, and it is 'knitted'. It would be worth anyone's time to learn, both crocheters and knitters.
If you cannot do the i-cord , and don't have enough yarn for double stranded crochet border, I'd crochet just an overcast edge, not even single crochet, something less noticeable than single crochet, nothing that will emphasize the thinness of the yarn.
And I like Anatares's suggestion, too!