Unfortunately this is not possible. Spike must run on the PC in which the BB60C is connected. You can use remote desktop like applications to control Spike from a different PC.
One alternative is to look into our SM200C spectrum analyzer. It uses a 10GbE fiber link from PC to device. It would be possible to run a long fiber cable between the PC running Spike and the spectrum analyzer. It would preferably need to be fiber/SFP+ end-to-end.