I believe that the Stagi Hayden's hand rail is neither a Brian Hayden nor a Wicki hand rail, but something dreamed up in Italy after a few too many glasses of vino.
I have not seen a Stagi Hayden, but if the hand rail is attached like other Stagis then, if you are prepared to drill one, maybe two new holes in each the face in of the concertina then it is very easy to relocate the handrail to a new orientation or position. The new holes will be invisible, but the old holes will now be on show. Tell folks that they are there to let the sound out.
Take an end off (just one at a time , please) and you should see two tiny wood screws holding the action board into the back of the end. Remove those screws and carefully pull out the action board (the board with the reeds on the inside and the buttons and levers on outside), set that aside being careful not to dislodge anything. Look inside the end and you should see two wood screws that attach the handrail. Remove those screws (or maybe just one if you just want to pivot the hand rail around to a new angle. You will need to drill new holes through the face that will line up with the existing holes in the handrail. I would probably us a strip of masking tape over the old holes and punch/mark the existing hole on the tape, you can then use the tape to locate the centers of your new holes. Drill from the outside in to avoid splintering the face of the end. Screw on the hand rail in its new position.
Now comes the tricky part: getting the action board back in place and the buttons located in their proper holes. Some folks do this by holding the action board with the buttons hanging down and offering up the end on to the buttons. I use a long, thin stick (e.g a wooden kebab skewer) to shepherd the buttons into place as I slowly drop the end down onto the action board. A bit of wiggling might help - that is of the concertina face, not you. If you are lucky then this works first time, are you feeling lucky? No, then you will just have to be patient, maybe very patient.
Screw everything back together, do not over tighten the end bolts or they will sink into the wood and look ugly. Just snug and a bit will do. Tighten the end bolts like you would the cylinder head on an engine - opposite to opposite working your way around until they are all home.
Now repeat the process on the other end.
Do NOT take both ends off at the same time or you might never figure out the correct orientation to put them back on again.
If you can, then I would be interested in seeing some photographs of the insides of a Stagi Hayden and of your final result.