So, when I set up this computer, I made the mistake of putting all my game files on my smaller hard drive. Does anyone know if it's safe to drag and drop the GOG folder to another hard drive without messing anything up? I've already changed the default hard drive for future issues. Thanks in advance.

There's no reason it shouldn't be "safe", and many of GOGs games can run without running a new install. I often reformat my computer and then I just move back the backup of both the game files itself, and selected config/save files that usually resides in the users profile.

Best case you might need to only set the proper drive (eks from drive d: to drive c:) on shortcuts, but there could be some games that needs to be reinstalled. Every game is different.

This should be safe as long as long as you are moving only games, not entire Galaxy folder.
To do that, close Galaxy entirely (click on the GOG logo located in top-left corner and select Exit), move your games folder to another drive/place. Open Galaxy and once again click on the GOG logo, select Scan & import games and point Galaxy to the place you've moved your games.
I'm not sure about desktop shortcuts, but Galaxy should import games without any problems.

^This, and if a game doesn't work because of registry entries point to the wrong place, choose Verify/Repair from Galaxy's More->Manage Installation.

I got it to work. Thanks for all the advise.