Dell used to have this with their Alienware laptops, but those days seem to be long since over. You're best bet looks like it's going to go the software route with a virtual KVM and network the mac and PC together. Software like Synergy will let you switch back and forth between the Mac and PC without needing the Mac Mini to be physically attached to the PC, or for the Mac to even have a keyboard/mouse hooked up.
https/symless.com/synergy
This will mean bringing a small switch along but if you're carting around a Mac Mini, you can likely spare the extra bit of space. You can get a gigabit one for around $20. I've used the software in the past, and it worked pretty well. The software was a bit twitchy on the Mac side, but this was also close to 5 years ago, so I would assume it's only improved since then.
*Edit There is also the options of capture cards. The Blackmagic may work for what you're trying to do.
https/www.blackmagicdesign.com/products/intensity
However, unless you're needing to be portable while overseas it may just be cheaper and easier to buy a monitor for $100 bucks. Since you're doing audio editing on it you don't need anything fancy.