You could plug your computer and laptop into a "home network" hub, like NetGear hub or LinkSys hub using two CAT5 cables. Then, share out your floppy drive on the old computer with the Mitchell floppy installed.
I have done this several times re-installing the Mitchell ShopKey software.
1) Create a folder/directory on the "new" laptop system called ShopKey.
2) Copy all the data that you have into this folder.
3) Run the install from the shared floppy drive.
When done, the install program will run and display a "key" and you will need to call Mitchell with this information for them to translate into a new running key on the new laptop.
Done!!
Hope this helps.