I need to drill holes to accommodate small screws to hang a soap dispenser.

I would use a diamond bit.
http://www.toolocity.com/Brazed-Core-Bits-Set.aspx?gclid=COShxPSL7JoCFRLoxgod3T-akA

I would agree but also suggest that you consider an adhesive like the one sold in auto parts stores for review mirrors. Once you get the hole in the mirror your cracking worries aren't over. When you install an anchor or molly you risk cracking the mirror when tightening the screws.

G4reat idea!