this is an entirely hardware specific issue and a little off-topic here,
I think.
But nevertheless: I had an installation where two Workstations were
attached to a BARCO, but the KVM System had no sufficient signal quality
for a good display - way back some maybe ten years. I suggested to
purchase another (high-grade) KVM and heard no more complaints.
Maybe you may just consider the hardware specs - pixel clock and KVM
Bandwidth, reflection and attenuation - take the Lowest Common
Denominator of both Workstations and the monitor, and give it some room
by adding some 10-20% room for extra image quality ;o) - and you should
be fine.
A cheap off-the-supermarket-shelf KVM will most probably not do, that is
what I can tell you now already. You need high-resolution and
high-frequency components for sure.
Hope this helps,
Peter