Disable SIP with third-party GPU

Yep. You can have your Apple TV learn the remote codes of any IR remote by going to Settings > General > Remotes. It will then ask you to hit buttons on your new remote corresponding to what it shows on screen.

Full instructions can be found at Apple's site: Controlling Apple TV with a third-party remote control

Edit: to answer your actual question, you can't do it from anywhere except Recovery Mode, so anything you do must be done from there.

Tested on a similar 4,1 upgraded to 5,1 [but I have a flashed graphics card so I could see what I was doing]

Reboot & at the chimes hold Cmd ⌘ R for about 10s.
Wait until you get to Recovery Mode, which for me took approx 45s from the chimes [I'm on SSD but I think it may have chosen a Recovery on another HD to actually boot from] Give it a minute or so just to be safe.

Fn Ctrl ⌃ F2 will switch focus to the menu bar, specifically the Apple logo, top left.

It appears that whatever you have set in System Prefs > Keyboard for "Use all F1, F2 keys as standard function keys" that this option is disabled in Recovery, so even though just Ctrl ⌃ F2 works for me in a running OS, in Recovery I needed the added Fn key.

From there, you can navigate using the arrow keys

Pic from https://apple.stackexchange.com/a/254167/85275

From that you can see that Terminal is 4 to the right, then 4 down.
It's 4 not 3 because the first down arrow opens the menu.

Hit Enter & Terminal will launch.
Type csrutil disable & hit Enter
Type reboot & hit Enter.

If it reboots, you got it right - otherwise you'll have to have another guess.

BTW, golden rule, as you have discovered, is keep your crappy old stock Apple card somewhere safe, for occasions such as this ;-)

Additional note: Fn Ctrl ⌃ F2 is a toggle. First will select the menu bar, second will deselect, so make sure to only do it once.