floating ground on ICs?

I don't have any idea how many do it but it is an accepted practice. Since you are building your own you can easily incorporate small switches in a pair so you can connect/disconnect the shield to see if it makes any difference. Some claim it even makes a difference which end is floating.

Either do it as Herman suggests -- but make sure the distance b/ween shield & wires is at least 2x the wires diametre and that it covers as best you can the complete length of the conductors to the connectors.\

Or just make them w/out shield and try out. CAVEAT: if you do that, don't leave a component completely unconnected -- i.e., when changing IC's, always have one connecting IC between components.

some have suggested a floating ground is a good idea - ie, connect the outershield to one end only, float the other

That is not floating the shield!
It is MANDATORY that you do so with single-ended cables, because connectong the shield to the RCA ground on both ends just creates a low-resistance bypass for the ground wire in that cable. Most shields are quite hefty relative to the hot and ground wires, so most of the "return" current will flow through the shield, if connected on both ends, rather than through the ground wire, as intended by the designer.
This bypass path will DISRUPT the correct operation of the cable!!! Many cables are designed with a balanced geometry so that the electromagnetic fields induced by the currents in the hot and ground wires actually cancel each other. The parallel bypass through the shield may not behave the same way - it will become more like a coaxial design.
It may sound fine, some coaxial cables do... It would be just a "funny" implementation of one...

BTW, you should mark the end where the shield is grounded, so that the stereo pair would be grounded exactly the same.