The method described here requires you to own a legitimate Steam copy of the game in order to run anything.

Thanks to the speedrunning community, we have access to an archived, pre-Steampipe build of the game, along with some convenient tools like RInput, adding raw mouse input to versions prior to Valve's official implementation of it.

Go to the SourceRuns GoldSrc Package page[forums.sourceruns.org] and download it; this contains the required build of the game.

Extract it, and install your pre-Steampipe mods to the Half-Life WON folder.
Then, make a shortcut to hl.exe and add the following launch parameters:
-noforcemparms -noforcemaccel -noforcemspd -game MOD_FOLDER_NAME

The first three will improve mouse input by disabling mouse acceleration and other overrides forced by the older GoldSrc engine, partially nullifying the need to use external tools like RInput. The last parameter will force the game to load your mod; as the example suggests, you need to put the name of your mod's folder in there, like so: -game CryOfFear

Now launch the shortcut you created, and everything should work!

Contrary to what the build's folder name implies, this isn't actually a WON-era build of the engine, this just has the older HL1 game DLLs to allow speedrunners to use old-engine tricks with the convenience of a slightly newer engine version.

You did it! You've now learned the forbidden art of running old engine builds and playing mods through launch parameters.

Keep in mind that certain mods, like the aforementioned PARANOIA and Cry of Fear require additional launch parameters. For example, the latter requires the following:
-heapsize 1536000 -num_edicts 4096
Due to the complexity of the mod, not using these parameters will make the game crash quite often.