As ArrGee has said, you can't run a program just by trying to open its file(s), which is what you would be trying to do. The program has to be properly installed on the computer that is trying to run it.
However, you could install the software on your laptop, as well as on your PC (I think most software licences will allow this), and then use the external hard drive to transfer your data files from one computer to the other.
However, if this is your only intended use for the hard drive, you're probably choosing a slightly clumsy way to swap the data files about. A little USB stick drive would serve just as well, and would be much easier to carry around with your laptop.
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