Kilayim 9:3

Shaatnez does not apply to hand towels, mantles of sefarim, or bath towels, though Rabbi Eliezer prohibits them. Shaatnez does apply to barber towels (because they are wrapped around a person like a garment).

Kilayim 9:4

Shaatnez does not apply to the shrouds used to dress a corpse or a donkey’s saddle. If a saddle contains shaatnez, one may not sling it over his shoulder for any reason.