Nah.
'United' and 'City' are (currently, if not historically) THE 'United' and 'City'.
Everybody (bar a supporter of one of the other clubs named United or City) would immediately understand who you were referring to.
Manchester United aren't even a proper "United". They've two clubs in their city, how's that "United"?
If saying "Manchester" first is too much of an effort, just call them "Man U" as we did throughout the 90s and 00s.