120VAC latching relay controlled by a low voltage momentary switch
Generally it's normal for controls like this, including latching relays, to run on 24V - either AC from thermostat transformers, or DC from batteries if reliability is required.   Lower than 24V isn't practical because you typically need to carry these control signals some distance.  

You can't switch 24V with an Arduino, but you can operate a fairly small relay that can switch 24V.    

This would be boring old trade electrical work, except that you made it harder on yourself because of your parts bin mismatch - 120V latching relay coils, vs low voltage switches.  So here you are.  What's the budget on this project?  

The preferable option would be latching relays with 24V coils, which are avout $30 each... Or if you're willing to do every inch of the control wiring in Class 1 wiring methods, you can get listed line voltage switches for about $10/pop (but this will do nothing to allow automation). 

If it were me, I would put 24V relays right in front of the latching relays, in the same cabinet.  That way you're doing the control wiring in 24V under the more relaxed low-voltage rules.