I have a 1972 UK MoD 1:100,000 map for the whole UAE, apart from western and southern Abu Dhabi (it's actually several sheets taped together, of course.)
This includes Sharjah, probably as it was a few years earlier when the data were collected. In fact, looking at some of the town areas, shown as black shading, I suspect that they are as they were in the mid-60s.
It's based on photosurvey overlaid with tracks and other topo.
You can probably do a lot better better, but if an A4 scan centred on Sharjah is any use I could provide it, towards the end of next week.
It would cover from Dubai to Hamriyah, more or less.