I've run a 4k monitor and a 1080 monitor simultaneously on a 7 year old Thinkpad P50 (m1000m gpu; wasn't anything to write home about when it was new) for years. I think you'll be fine with an old laptop.
I've run a 4k off an x220. It had to run at 30Hz, but it otherwise worked way better than I expected (which was not at all).
Maybe an external video card will work? But to really utilize that it would require a laptop with a Thunderbolt port which is out of the question for most old laptops.