I have a nice (but not nice as yours!) short strand of amber beads that I am struggling with...the variation in the hole sizes makes for much of the challenge. But I am stubborn, and tend to wear them anyway, at the moment stung on a wide camo-pattern shoestring! The stiff flat shoestring seems to "spring-fit" the varying hole sizes, if that makes sense...but it's just "for now"!

I have used shoestrings often -- mostly with African trade beads or the like -- and it works very well, it keeps in place beads with larger holes, while going trought most of the smaller ones.
Of course, there are myriad ways of reducing the size of the VERY large holes too!