I walk a lot on my own in the Peak district. I am more wary than a man might be, especially when I'm doing a new route but generally feel and know that I am safer than walking around town.
I prefer being in the open, where I can see people coming rather than woods, but I think that's the fairy tales! I am also more aware on routes where there isn't an easy get out, so an enclosed canal path isn't my thing. However, I also take this advice for cows!
I sometimes do get a scary feeling (more panic like) with exposure in a wide open space or I think that I'm miles away from help if something does go wrong. I find chewing gum helps with that- gives my mouth something to do and regulates my breathing.
I am more worried about twisting my ankle and being unable to walk on than being attacked but there are many steps I take to minimise any risk
*I carry a bivvi bag (even in Summer) and extra food and water
*I tell someone my route, however rough and what time to expect me back
*I also use the OS map (and carry a proper map, compass and whistle)
*I try and be aware front and back of other people, there are usually more than you realise. Trust gut instincts- most will have walking equipment (though fell runners often travel light)
*Try and look confident and if you know where you are going. Unless of course you really are lost, then it's usually best to ask
*I talk to everyone enroute (this is partially a Derbyshire thing and partially a walking thing). This helps me realise that most folk are like me, out for a lovely walk and not a murder. I find single men walkers have tended to be very respectful in not frightening me if they overtake
As a PP said, start small. Perhaps always do a new walk with someone before undertaking on your own. I love the space and empowerment it has bought to me and my MH.
Also search for an Adventure Queen local group on FB. These are more individuals rather than an organised walking group.