Some devices have physical kill switches for cameras and mics. Whether or not the eavesdropping theory is true, such devices can help you deal with your immediate worries.
Failing that some tape works quite nicely!
QubesOS allows you to assign certain devices to Xen VMs , compartmentalising your hardware. No spying if there is audio/video device (a Xen hypervisor escape not withstanding) available to the guest OS.
I do like devices with physical kill switches. Some USB sticks and devices by Purism.