Does a 1ms 144hz+ G-Sync Monitor w/ HDMI Output Exist?

[Cools]

This is hard to explain but I'll try. I play comp CoD primarily, which is restricted to PS4. I'm planning on getting a PC for some gaming, but I'll still be playing CoD on PS4 primarily. I currently have a BenQ rl2460hm(discontinued), it's a 1ms 60hz G-Sync monitor, less than ideal for PC gaming, but all you need for console. Neat part about it is that it has an HDMI output port on it, which is the only way I know of to record off of console with 0 added delay. For my PC, i'll obviously want to utilize a 144hz+ monitor, the goal being to have my PS4 in HDMI 1 and my PC in HDMI2, and then a second HDMI linked from my PC to my 2nd monitor(not even sure if PCs have 2 HDMI outs). Problem is, if I do this and the monitor doesn't have an HDMI output, then i'll have to run the PS4 to the capture card(planning on getting a 4k60 pro), and the capture card to the monitor. I might be wrong here, but that must add a delay from the PS4 to Monitor, however small it may be. I'd like to avoid this if possible, because even if it's incredibly hard to notice, I don't like the idea of hurting my gameplay on my primary platform in order to play PC games how they're meant to be played. Any help is appreciated, I've been stumped on this for a while.