cut-throat razor 
noun British
A razor having a long blade set in a handle, usually folding like a penknife.He was so hard - he had two little pockets sewn into the end of his coat sleeves… And in those little pockets he hid two razor sharp, cut-throat razors....
- I paused as he put down the clippers and picked up his razor - a steel cut-throat razor like something out of a fifties gangster movie.
- The local men always had the barber shave them in that period, with the cut-throat razor as the stainless steel Gillette or Wilkinson blades were not around then and Philishaves were not very plentiful yet.