Hi Bob, why are you using your personal laptop at your desk instead of the company's laptop?
I have never hidden the fact from any of my management in any of my companies that I interview with other companies on a semi-regular basis.
It reminds them that while I am a replaceable cog in their machine, I am also a cog that other machines would like to install given the right opportunity. And I am always aware of my current market value.
If you are openly interviewing for other jobs from your desk I don't think which laptop you use is going to be anyone's concern.