According to the American Red Cross, one should never do a 'Blind Finger Sweep' in a choking child--you should only remove the object if you can see it.
This should also apply to other things, such as:
Yesterday morning when I got Charlotte out of bed, I felt something small and hard in the back of her jammies. I asked Randy what he thought it was, and (judging by the size and texture through her jammies) we concluded that it felt like a Cheerio. So, I went in with a 'blind finger sweep' and came out with not a Cheerio, but a dried-up poopie ball--just the size of a Cheerio! Apparently, it had slipped out the top of her diaper sometime in the night.
So, after a good hand-washing and sanitizer later, I can safely say that the Red Cross has it right! NEVER do a 'blind finger sweep!'