Umm, if your bootloader is unlocked you could flash a kernal with a recovery and flash the ROM that way. but you would need Android SDK set up..which can be a pain.
try find a tft file of the update and flash that with Flash tools.
here is a link to the tft file.
Xperia S_LT26i_6.2.B.0.200_Central Europe_Generic | Xperia Forum
but be warned, i have never used this site, i will not be held responsible if you fubar. I will however, try and help you if the worst is to happen.