Here are download links for ver. 1.75. I suppose it's the last version of the patch.

full version

minimal version (patch+subs)

Yep, it is latest version.

Cool.

I've been trying to install the available version of the patch from PC Gaming Wiki, but the installer wants the CD image. How do I get around this?

Full version is an archive of all needed files + launcher-installer for remain game files. Just extrqct acrhvie - optionally installer - and use another one exe.

Try download it from link above for latest version.

AppCompatibilityChecker by Verok
http://disk.yandex.com/d/37-Y0GVgWUATJA

it cannot remove compatiblities installed by sdb-packages (ms ACT\ADK app)(installed with the game by DISMM service - cmd window appear duting installation of the game).
But this tool can show it. Use WinRegistry and manually clear Windwos system some sub-folder. Or dowanlod ADK (ACT 5.6 for Win8 or eallier) to remvoe it.

look to .sdb files.

There is sdb file in ingame folder. You can open it by WordPad or HxD and look where it stored.

You need to run setup executable with the ISO of the game mounted - so it won't work with GOG's version

Setup not needed there at all. Well, at least for few latest versions. Just put it to the game folder and run normal kain.exe. Launcher will appear.
So it is working with GOG version initially and updates made some tweaks to make it more easy. At least since then wrapper both full and lite packages can be just extracted to the game.

Getting back to this game, still trying to get the Verok's patch to work...

Since on my laptop the webcam is integrated, I can't disconnect it, but I disabled it instead in the control panel. No effect for me.

It could certainly be some other connected device as well.

I think Hovenduck had the same issue as me, ie. the vanilla GOG version works, but with Verok's patch, there is a control issue, ie. the player will constantly move to NW.

I tried your suggestion, ie. renaming dinput.dll and ddraw.dll to something else before applying the Verok's patch, but it had no effect. Still the same issue.

I've yet to try this on some other PC.

Mmm, maybe Steam client in background? Steam Input applied when Steam client launched and detected gamepad plug-in. Or actually just launched, it not even wait for gamepad. And few years it was completely broken (cause even Keyboard Letters-input disarming, without gamepad plugged in!).

Should work for Xbox pads or close clones (or Dinput/Xinput switchable in any mode). Support for Sony pads relay on HWID and most likely Verok did not make all HWID supported (cause so many pads, wired and wireless detected as differ devices, Sony sometimes change HWID with new revisions of same gamepad). Additional Sony pads unofficial wrapper's are probably better, and not sure how it will work with Verok. Probably better turn off Input wrap'ping in INI file, if there is such option there or in launcher.
For Sony pads still better keep them for Sony consoles.

Both GOG and Verok input wrappers are as a wrappers still not a native support for Xinput (or more modern Dinput than in original game). Some features standard nowadays can be unsupported or working wrong/glitched (eg no hot plug-in during gameplay).
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Everyone here did not use Program Files folder, right? Never mind. Game settings and as I remember Verok wrapper (there is no actually an INI) use Win Registry. Original Retail use HKLM. Maybe better keep exe in run as admin mode? Theoretically VirtualStore as always should be used instead and working fine after second launch (first one still better in admin for clean GOG game). But I saw already few times on differ forums that Win Registry ignored. One of such cases in Heroes sub-forum here.

There is tweaking in Windows (in Registry,yep) to disable VirtualStore. That must be used as addition to disabling UAC. Keep one enabled make troubles. Maybe it cause of repacked (wares) non original Windows 10 distribution?
Anyway. Better keep UAC as is. And in Default state: Enabled with blocking Desktop for it pop-up ptomts. Even disabling just UAC cause more issues than solve - cause it not disable VirtualStore using (separate option hided in Registry).

Game path are strictly *non-C*/Games/Game-name-1/. I doubt there is AV/security apps make Registry ignored for apps from such folder. There is no admin mode required. But for Program Files maybe there is AV ignore runasadmin and keep some files in game folder ignored as well as Registry in case if GOG's version still use HKLM (Heroes 3 case are similar - game+GOG version use HKLM for settings)

So, what I want to say. Maybe for Verok wrapper game shouldn't be started before wrapper install? If this somehow in some way issues with settings in one or both HKLM/HKCU /Software/LegafyOfKain/ section (GOG version use non original changed exe, saves folder are differ, settings path probably too).
Maybe try to remove REGEDIT entries and restart wrapper. Also there is should be Reset function for settings in wrapper launcher and/or ingame menu (in Windowed-Windowed window mode).
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One of the non-mandatory non-native function for input wrapper - binding. Any gamepads - you should re-bind controls manually. Same as on Dinput General PnP devices in any old Dinput games. The only case when it not required are original Ms's Xbox pads in native Xinput games. And maybe sometimes it also become required for Xbox pads (and maybe wired/wireless as one device also been no more mandatory, or any else nowadays standards, decades after with more pads variations) Input settings same as any else game+wrapper are stored in Registry. There is some options tweaks available only there.

Yes, this is correct. The latest version of Verok's GL wrapper & patch (1.75) does work with the GOG version of the game. I downloaded the full patch from PCGamingWiki and then extracted it to the main game folder and replaced some files when prompted. Then I just launched the game through Galaxy and the setup appeared. The game works fine and even my Xbox Series X gamepad works (button prompts and all).