This is what I would do:
1. Strings
First thing to do is try higher tension strings. It is OK to use Tenor ukulele strings on a Soprano if you are going to tune down to B-flat tuning.
This should be the easiest fix requiring minimum modification to the ukulele, and the higher tension will improve the sound of your B-flat tuned Soprano anyway. You may go through several different brands before finding the one that works best for you. Personally I think Fremont Fluorocarbon or Worths should work.
2. NEW Saddle, NOT Shim!
Shimming is absolute last resort. In fact, I don't think it's good practice at all in general.
Others may disagree, but over the years, I have found that it is much more practical to just buy new saddles (I prefer bone saddles) on eBay and sand them down to size based on the current saddle. I usually order a few saddle in case I mess up with one, or want to experiment with different saddle heights.
Negative experiences I have had with shims:
-They should be a dense material like brass or hard plastic. I used to use old credit cards, thin plastic, etc - but it is darn difficult to cut a shim into the narrow shape needed!
-They may affect your tone. Personally I think paper/cardboard is a poor choice of material, as they are not very dense.
-Harder to fine-tune your saddle height compared to being able to sand one down to the precise height you want.
If 1 and 2 fail, then it starts getting more complicated.
Nut problems are a bit harder to fix, as you need to punch the current nut out safely and install a new one that isn't filed down as far. You also need nut files and some experience with nuts in general. Sanding a saddle down is relatively easier since you're just adjusting height on one surface.
Some people advocate using superglue as a nut-slot filler. I haven't found this method to be very elegant, as dried glue is not as hard as the nut material and wears down after time. It is difficult to fine tune the shape of your nut-slot with glue. Furthermore, it is not a very "permanent" feeling fix on a good uke.
By this stage, I would consider trying this tuning on a new ukulele, perhaps a tenor.