Probably some Scotsman's pronunciation of shirts. It is not 'shi ya', it is 'sha' (notice the small ｬ）. It could also be because Japanese would have simply had trouble distinguishing between the vowel pronunciations that can vary even among native English speakers. As there is no differentiation between singular and plural with Japanese nouns, it could just have easily been シャト.
So, a dialectical pronunciation for 'shirts' that sounds like 'sharts' became シャツ.
Incidentally, Shi ya thsu is a type of massage：）