You can update the skin via sql yes.
if you run this script in the sql window you can see the skinSrc currently in use and the ContainerSrc. These values are what gets set in the page settings.
Select * from tabs
That will display the contents of the tabs aka pages table. NOTE: Some people / hosts tell DNN to put a prefix on the tables in the databases. If so you need to add the prefix to the tabs part. so: Select * from prefix_tabs
If you have direct access to the database its easiest to just go in and manually "copy" and paste the values you want onto the rows / pages you want. So if you want pages x,y,z to all use the skin named EnglishTeacher. You just open the table and make the changes to the skinSrc column.
OR if you dont have access you can do something like.
update tabs Set skinSrc = "value for the skin" where TabID = <tabid of page to be updated>
You can get both the value for the skin and the tabid from running the Select * from tabs results. Or you can run this query to get the different SkinSrc : Select * from skins.
You can zing through a ton of tabid's / pages in a quick succession if you write all them down that need a particular skin.
Can copy and paste the same code multiple times.
DISCLAIMER I HEREBY ADVISE YOU WITH ALL THAT IS SACRID TO BACKUP YOUR DATABASE BEFORE RUNNING ANY SQL COMMANDS AGAINST IT. YOU HAVE BEEN WARNED.
The code is sound but if you mess up the tabid, or mess up typing in the skin's path etc and you don't catch it right away it can be a pain to recover from. Its possible but a pain.