Is it normal to have a light switch setup using only the hot wire?
Yes, this is normal.  There are two ways to wire a two-way switch with 2-core cable like you have: 


one where the switch is between the supply and the light fixture(s).  This is how your switches are wired.



As you can see from the diagram, the white wire is used -- it completes the circuit back to the electrical supply's neutral line.
one where the light fixture is between the supply and the switch.  I think this is what you mean by a "standard black-white setup".



Note that the white wire in this case must be marked to indicate that it is carrying the electrical live; I use a small piece of black electrical tape wrapped around the insulation.  It's common (in my experience with amateur wiring at least) for this step to be omitted.


(Images found here)

If you change the switches, you should follow the original wiring.