What a cute quilt! And totally irreplaceable, so I think your caution is merited.
I have only used 100% cotton batting a couple of times, and I always washed (soaked, gentle spin) it in very hot water. Since I didn't measure it before washing, I'll never know how much/if it shrank.
Only once did I use a natural batting (100% wool) and not wash it, and it was a disaster - the batting shrank so much that the quilt was actually distorted, and I ended up unpicking the whole thing and doing it again. It was just a crib-size, but still! I am now very paranoid about shrinkage...