The holes look threaded. If so, are they imperial or metric? If imperial, they are probably 6-32 or 8-32. Although the fit is not perfect, it is said that M3.5x0.6 and and M4x0.7 will fit those sizes, respectively. If that fails, you could drill to the max diameter of the thread* and use a smaller metric bolt. Since you do not know how thick the walls are, I would be cautious using the bolt you show given the cost of a new switch. A few thousandths (inches) oversize will probably be safe.
If the wall is breached will it damage the switch? I don't know, but judging from the corrosion on the lever, I suspect that would not be a good idea.
*Outer (major) diameter of those imperial sizes are readily available.