Once I go through and delete all the low search volume KWs how do I go about deleting the corresponding Ad groups and Ads, as those are still in my account?

You can do this two ways: Adwords Editor or in Adwords account. In account, go to top right notifications (bell symbol) and you should see a warning that you have ad groups with no KWs in them. Click on it and you can manage those ad groups (delete in this case) from Adwords. In the editor, you sort the columns by using the circle notifications top left of the main box (while under Ad Groups). You'll see all the errors (in red) and what the error is at the bottom of the main box. Select and delete all the ones that are errors because of no KWs in Ad Group.