“The Gemara in Shabbos (75a) says that according to Rabbi Yehuda, one who extracts the dye from the chilazon on shabbos is chayev for Dosh. Now the minimum shiur to be chayev for Dosh is a Grogeres. The amount of dye taken from a Murex Trunculus is less than a Grogeres.”
I will argue that high value items can have smaller measures for which one in liable on Shabbos.
The best that I can recall, different fluids have different measures for which one is liable for carrying.
For most items that are threshed, the size of a fig is needed to have value. High value techeiles dye should have a much smaller critical mass.