This is from my experience so far today testing out wether Saints Row 4 Re-Elected runs without the epic launcher or not and thought I'd post this as there doesn't seem to be any info on here mentioning this

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I Installed via Galaxy and clicked play, it then asked if I wanted to allow the epic games launcher to install, I clicked no and the game booted up fine and the epic launcher was not installed to my PC

I then tried installing via the offline installers to see if it installed the epic launcher during the process, it did not and I could launch the game fine and play via clicking the sr_hv.exe in the games folder

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Important Note

Make sure that when you install or load the game via Galaxy that you change the default executable it uses for the play button, the current default directs straight to the epic launcher installer, setup a custom executable targeting the sr_hv.exe in the games folder to bypass the epic launcher install request

For offline install without Galaxy, just create a shortcut for the sr_hv.exe in the games folder or edit the existing shortcut to target the sr_hv.exe and use that

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Of course if you wish to play online with others then you will then need to install the epic launcher

So far i haven't had any issues with this method