Don't hesitate to take the locks off. It was made for that purpose.
Just remember the locks must be cocked to take them off and put them back on.
One slick trick is to fully unscrew and remove the lever headed bolt that you refer to, then take it around to the right lock and gently screw the threaded end into the hole where it came from. That gives you a "handle" to wiggle the right lock out of its mortise. The left lock can then be very gently coaxed out of its recess by gently tapping the heads of the sear levers through the hole using a small wooden dowel.
Just be very gentle. You don't want to pull a wood chip from the edge of the recesses.
It's really a lovely shotgun and beautifully engraved. Rest assured the Italian workmanship is second to none. Here's a shot of my 20b Piotti Monaco No. 1 (with Majestic engraving):

My interpretation: the lion gargoyle's roar is represented by the elaborate scroll work emanating from his mouth. You can almost hear it in your mind.


Curl