If you cannot find a string mop that is narrow enough, you can make one using a ball or two of cotton knitting yarn and a stick.
Cut the yarn into lengths twice the length you want each string to be and fold them over. Gather a suitable number of them into a bunch, insert the stick in the middle of the bunch then tie the mop-head firmly into place with one or two lengths of string or yarn.
Sorry I can't attatch a photo, but the site will no longer accept ones taken on my phone - they are apparently too large.
This is how I make dolls' mops and feather dusters and it is, as far as I know how mops were made. My dolls mops and washing up brushes can be used, so this larger one should do the job too.