How to composite live 4K video with prerendered alpha matted footage
I have a Blackmagic Design DeckLink card which, with bundled software, provides live keying.  I bought that card before they sold a DeckLink 4K cards.  But because they come withe the same bundled software and make the same live-keying claims, I would check that this version first: https://www.blackmagicdesign.com/products/decklink/techspecs/W-DLK-04

You should be able to ingest two channels of 4K video, key it, and output the keyed result in real-time, for $995.  It does require you to have free PCIe card slots in your computer.

An entry level 4K switcher (that gives not only pre-rendered alpha matted footage, but also transitions and chroma key) runs $1,695, and runs stand-alone (i.e., not a card in your computer): https://www.blackmagicdesign.com/products/atem/techspecs/W-APS-04