Word Origin and History for in one's shirt-sleeves
Old English scyrte "skirt, tunic," from Proto-Germanic *skurtjon "a short garment" (cf. Old Norse skyrta, Swedish skjorta "skirt, kirtle;" Middle Dutch scorte, Dutch schort "apron;" Middle High German schurz, German Schurz "apron"), related to Old English scort, sceort "short," from PIE *(s)ker- (1) "to cut" (see shear (v.)).
Formerly of the chief garment worn by both sexes, but in modern use long only of that for men; in reference to women's tops, reintroduced 1896. Bloody shirt, exposed as a symbol of outrage, is attested from 1580s. To give (someone) the shirt off one's back is from 1771. To lose one's shirt "suffer total financial loss" is from 1935. To keep one's shirt on "be patient" (1904) is from the notion of (not) stripping down for a fight.