Tse-Che-Nako's Weaving uses terminology "this shaman".
Matthew Rising Sun isn't a shaman.
Can he use the totem, and what happens if he does?
Matthew Rising Sun is not a Shaman.His text specifies that he does not gain Shaman while casting a Totem.Therefore he cannot use Weaving or any Totems that refer to the casting Shaman.
Additionally since Kung-Fu isn't a skill, an attached Tlalocs Fury has no effect on his ability to cast Totems.