I wonder if you mean safety from crime, or safety from traffic? In my experience, Brits are usually surprised at how safe they are from crime here in the U.S., and also surprised at how unsafe they are from traffic. Very generally speaking, you will not have to worry about crime, as long as you stay away from the inner cities - and if you are touring along the coast, you are by definition staying away from the inner cities.
As far as traffic, though, I think you might not be too happy. Cycling along the coast generally includes riding on Pacific Coast Highway, many parts of which have poor excuses for bike lanes, along with 70 MPH traffic. Honestly, there are very few cyclist fatalities even on PCH, but you are unlikely to find that part of your tour enjoyable, based on input from Brit friends of mine.
Short version: You are almost certain to be fine. In my experience Brits tend to come to America with visions of daily gunfights and are surprised to learn that violent crime is actually very low in America, big cities excepted. Go out of your way to find campgrounds as far from the beaten path as possible, and you will be very happy. The traffic on the major thoroughfares is intimidating at first, primarily due to the very high speeds, but there are lots of cyclists in this part of the country and motorists are used to them. Once you get used to it, you should be able to largely put it out of your mind.