Totally doable - I run off of an external myself - I just link the mod folder via this method (taken from Reddit):
1. Move your Mods folder to your external hard drive by clicking and dragging it from Documents\Electronic Arts\The Sims 4\ to the external drive while holding shift. Ensure that the popup that appears says "Moving files," not "Copying files." Once this step is complete, you should not have a Mods folder in your Electronic Arts\Sims 4 folder but you will have one on your external hard drive. If you want, you can rename it to something else to make your life easier (eg "Sims 4 Mods" rather than just "Mods").
2. Press the Windows Key and X at the same time, and click "Command Prompt (Admin)". Paste in the following command:
MKLINK /J "%UserProfile%\Documents\Electronic Arts\The Sims 4\Mods" "[insert path to mods folder on external hard drive here]"
Make sure you replace [insert path to mods folder on external hard drive here] with the actual path to where you copied the mods folder onto your external drive (eg. "F:\Gaming stuff\Sims 4 Mods").
3. Go to Documents\Electronic Arts\The Sims 4\Mods in the file explorer. If you see all your mods, that should mean it worked. Run TS4 and check the options menu to make sure your mods are showing as installed, but do not load any of your saves before checking or else they could potentially become corrupted.
If all goes well, this should create a symbolic link in your EA\TS4 folder that points to the folder on your external hard drive.
