How can I switch multiple lines using a single switch?
You may actually be able to do a lot better than having to switch 34 wires.  Take a look at the floppy connector pinout:

http://www.interfacebus.com/PC_Floppy_Drive_PinOut.html

First of all, half of the wires are grounds, which you can just connect in parallel.  Secondly, the cabling is actually designed for two drives to share the same cable, with a 'twist' in the cable to differentiate between the drives and all of the other connections wired in parallel.  What goes through the twist are the drive select and motor enable signals.  You might be able to get away with a simple DPDT switch to decide which drive gets connected to the drive select and motor enable signals, and connect all of the other signals to both drives.