Rough beveled edge face on Travertine cuts?

We are tiling the terrace and Gazebo floor with some Travertine. The
Tiles come in odd shapes (a pattern) and the edges of the tiles are
rough cut rustic beveled.. They are a perfect 90 degrees, but the face
edge is beveled rough,

Is there any tool or technique to simulate the same rough edge bevel
on the cuts we perform? If not, we might end up with some edges rough
beveled and some with a razor edge. Another concern with a razor edge
the risk of bodily harm. Travertine is a solid rock so one plus is
that if over time the edges chip or wear it will continue to have a
very natural look.

Thanks for any help or information!