Around here there are at least 4 paths that have dual designation of pedestrians and bikes shared without markings as there are near Rye Harbour. I have never heard of any problems and there won't be as long as the cylists and pedestrians (with their dogs) aren't idiots!
Several pavements round here are designated for both cyclists and pedestians, as long as either aren't idiots then there is no problem. There have been no casualties that I have heard of over 10 years.