The "Con Safe" Bow is practically a myth.
Every Convention has different rules, thoughts and staff. Some say unstrung bows only, and yet while there you will see SEVERAL compound bows, and recurves. Myself, I went to two very large conventions recently with my Arrow Costume and took my Season 1 bow. Zero issues strung. They checked the ARROWS more than the bow. I did Dragon Con in 2012 with my PSE Mojo Smallville bow, also strung, also no issues. They also checked the Arrows.
Realistically that would be the issue anyway. A strung bow is no more dangerous than a foam sword without arrows. The one largest convention wanted to Weapon check my PKE Meter, though...
The point is, there is no such thing. If they want to, they can send you on your way with a fake PVC-limbed bow, or custom foam weapons. One convention stopped someone with a fake baseball bat and foam nails in it, but allowed Airsofts. It is a mixed bag, but don't ever think that one option is more con safe than another.