The edge of the DE blades tend to stick out of most razors although there are some, as mentioned, that will enclose the entire head in the silo.

There are a couple of other options available if you want to stay "classic". The Shick Injector, Ever-Ready, and or Gem - single edge blade, no protruding blades. The Injector, particularly the "newer" models, may be more leg friendly due to the head geometry than the broader and wider head of the E-R and Gem.

In the bottom row beside the straights: Ever-Ready is on the left, Injector on the right