It's funny I've been trying to get a good shot of that "blue tool" after searching for more pics of the snap knife. It shows up on Picard's desk quite a few times.
My best guess is that it is a version of this medical tool I found form an old auction-
Ooh, great reference shots! Ryan and I have been talking a bit about that desoldering tool but you've found more of its appearances than we did. The auction pic is likely one and the same.
Another blue desoldering pump was later cut down and modified to create a Voyager prop: