So seeing as we stupidly can't disable/enable dlcs like we used to be able to going back as far as Morrowind I have instead gone into the following folder:-

C:\Program Files (x86)\Steam\steamapps\common\Skyrim Special Edition\Data

and moved the Dawnguard, Hearthfire and Dragonborn esm files into a folder on my desktop.

This seems to have removed the dlcs from the game. I tested this by using a console command to try to add an item that was part of Dawnguard. This command worked before I removed the esms but not after indicating they were removed.

However I have noticed the bug were wolves in the game do the howling animation but don't make the howling noise. This was a known bug in Dawnguard. Is there anything else I need to remove besides the esm files or are issues such as this now mingled into the core files?

Does the bug occur on a new save file as well?

Yes it does mate. It occurs on a fresh install. A bit worrying based on how many bugs were in the regular edition

Really was just a stab in the dark. I'm not sure then. :/