An advertising screen in the city included Satday 13 June in the corner. If there isn’t enough space for Saturday, then surely the solution is to use Sat. Sunday, Monday and Friday have six letters and would fit, but Tueday, Wedday and Thuday look varying degrees of weird. I’ll have to go back there on those days to find out what they do.
Saturday is already truncated from Old English Saternesdæg and Latin Sāturnī diēs. Many people pronounce it as or close to Satday or Satdi.