There are very small needles, the size of the needle is not the issue, the fact that their veins are very tiny is, and all of the ideal places to find a good one are in usable pelt areas. Before a pelt is used it must be blocked ( basically squared and stretched) if there is any hole or rip ( which should be stitched by hand after pelting if there is any ) it has the risk of tearing completely open. A chin pelt is so thin it is not like cowhide leather. Any holes or rips lower the pelt value because it makes it harder to work with for the furrier. Plus anytime you stick a needle into a living animal you have blood come back out, even in small amount. The more they squirm the more will come out, or if you don't hit the vein right on. Plus are the chins going to lay there willingly for this to happen? Chances are they would need some for of sedation, again raising the cost of process. Not to mention the difficulty, people want to be paid for their time and efforts.
Other than the rarity of a transfusion what else would chin blood be used for?
I personally have never heard of a chin dying because they did not have a transfusion. The ideal thing to do would be to know other people with chins, like Dawn said she was prepared for one of her other chins to donate if it was needed.