You should try walking in the dedicated cycle paths because cyclists NEVER use these so you'll be cyclist free and safe.
Zooming UP Coldean Lane? Don't really see that. I cycle up and down Coldean Lane most days - don't see it as particularly scary. Not sure it's the way I'd go to Hangleton though; it may be the most direct but Lewes Rd, Upper LR, Preston Circus, Dials and OSR is more cycle friendly. That's the way I went 30 years ago when I had a girlfriend in Hangleton