Is there an option to top load? Subcontra strings through body is going to be difficult. A 5 string bass with string through body only is a bad design.
Consider: what's the distance from saddle to ball end? If the ball ends are anchored deep in the body that distance may not be much longer than top loading, so you may still be able to use a taperwound string and have the taper on the saddle. However CKS' taper is super short so check out Conklin Snakeskins .165 or Pyramid .160: http://www.conklinguitars.com/bass_strings.html http://schneidermusik.de/shop1/advan...a4qqlbtthim0o4
Also consider if your string holes are wide enough to pass a .160 through.
For the minimum practical tension of 30 pounds, extra light, you need at least a .160.