Removing the Y caps from the laptop psu may help, but may be difficult and may invalidate guarantees, certificates, etc, and might increase rfi beyond spec.
Be wary of switching both poles. If signal is connected while ground isn't, your amp would probably see half mains voltage on its input.
Grounding your laptop 0v dc line to the desktop's earthed case may solve your problem.
One option if all else fails might be to use an amp or preamp with differential inputs.
NT