I'm not an expert either but from looking at your cute pics of Tillie she looks like she has a silky coat. Izzy has a silky coat and don't get mislead that just because your Yorkie has a silky coat that she won't mat. Izzy mats still under her legs (where she squats) just not as bad a cotton coat would (I used to have two males and one was cotton and one was silky). The cotton coat was harder to grow and maintain so we kept him in puppy cut all the time.
Hopefully the real "experts" will post for ya!