To get the load time remover working for Livesplit you need to run the game with a very specific .exe file. It is available in this downpatch rar: https://www.dropbox.com/s/t84pbp3t2rywowh/SW%202.1.4.9%20to%202.0.0.1.rar?dl=0 That is a downpatch for the gog version of the game from version 2.1.4.9 to 2.0.0.1, just copy the stuff from that link to your game folder and it should work.
You can use that patch on the steam version of the game aswell, copy the data folder and sw.exe into your steam shadow warrior folder. Do not run the game through steam, start it from the folder and you should have a working 1.0 version of shadow warrior. You may need to delete the shadow warrior saves/config folder in your documents folder to get the game to work properly(or even reinstall the whole game).
If you happen to have a cracked version(1.0, check the version of your .exe) of the game you can(hopefully) just replace the .exe with the one from that link and the load remover/game should work(I would suggest making a backup before doing any of this).
If you have any further questions, I don't think I have the answers.