I found riding through "dangerous" parts of town to be fairly safe. By the time the bad guys have seen you, you have gone, and a bike doesnt mark you out as a high value target. The thing to watch for is getting punctures in those neighbourhoods.
Do everything you can to toughen your tyres. Use a Kevlar slick tyre of sufficient width. Add Mr Tuffy tape if the streets are in bad condition. Try and vary your route a bit, so you dont pass the same corner at the same time every day. Carry a mobile phone, or make a note of the location of any public phone boxes you might need, and carry the number of a taxi company just in case.
Try the route on a Sunday and see how it feels.