Shely 1L with staircase timer

I wanted to add a shelly device so I can switch on the corridor lights in my building in certain scenes. We have on each floor several regular physical momentary switches with 2 wires and an indicator lamp. The lamp is on when the switch is not pressed and turns off while the switch is pressed. I wanted to add a shelly 1L in parallel with one of the switches. The live terminal would be connected to the live wire, and output to the output wire switch. Note that there is no neutral wire here. The relay would be on for 1 sec enough for the staircase timer to switch on the lights, simulating a press on the physical switch. Would this work? Or is there another way to do this? I think I could access the actual timer switch in the building and put either 1L or any other switch from Shelly, but the first method is more accessible.

Kind regards and thanks in advance for your answers

Ok, but where should I put the bypass, on the terminal of the staircase timer?
Or maybe it would be just better to wait for the Pro line and just put it as a momentary switch?