Style Designer Group
 

How do I create a usergroup with only access to the style and templates part of the Admin CP, without making them an admin?

You need to give them access to the admincp in order to give them access to the styles and templates area.

Something you could do instead is create a test site and have them do the design on the test site - giving them access to the Styles & Templates there. Then export the style from there and then import it to the live site.