The solenoid is going to be the fastest and least expensive...
And it is the contacts in a push button switch, that could weld together... If the switch is rated for the current that will not happen... usually.
It is possible for the same thing to happen in a solenoid, but that is extremely rare & usually involves a failed starter or other direct short, like the cable between the solenoid and starter shorting to ground.... Either will cause the current to be a lot more than the rating, and nd that can lead to a welded contact situation...
In any case going back with the original type solenoid will be easy & safe... :smile:KennyV