Hey I tried using SWP however whenever I launch it, it gives me an error stating "failed to load tables.dat"

What do I do?

Same issue.

While I used to use SWP source port all the time, it has known bugs (mines no visible) in Shadow Warrior.
I would recommend trying one of these:

Raze
https://github.com/coelckers/Raze

or

BuildGDX
https://m210.duke4.net/

I like Raze, as it seems to follow GZDoom start up menu aesthetics, and will find GoG installed versions automatically (well, it should anyways, but can always point it there).
BuildGDX is easy to "point" to any of the games it supports as well. It may also auto find GoG installs, but I never tested that.