Yes, Cyper WP is labeled to kill fleas and it's safe to use inside and outside. It can only be used on baseboards, cracks and crevices inside your home. The 1 lb jar has been discontinued though but we do have Cyper WSP or Demon WP available, these products are also safe on pets.
I would, however, recommend our Outdoor/Indoor Flea kit. You can use both, Onslaught insecticide and Martins IGR, in broadcast applications inside and out. Meaning you can use it on your carpet as well for a more thorough treatment. Both products are also safe for everyone as long as you follow the label instructions and let the area being treated completely dry before letting everyone come back into that area, including your pets.
Cyper WP would be a great choice for indoor and outdoor spider control. The active ingredient in Cyper WP is cypermethrin, which is known to be one of the top choices for spider control. Spraying Cyper WP will also help to get rid of the insects that spiders feed on and that will help to stop new spiders from moving in. Indoors, spray around all baseboards, door frames, window frames, under appliances, in closets and storage rooms and in areas where utilities enter into the structure. Outdoors you should spray around the bottom of the foundation, on the ground adjacent to the foundation, door frames, window frames and places where the utilities enter into the structure. We have included Cyper in our spider control kit, which also contains glue boards to help monitor the infestation (and help catch the spiders too).
Cyper WP: http://www.domyownpestcontrol.com/cyper-wp-p-228.html
Spider Control Kit: http://www.domyownpestcontrol.com/spider-control-kit-p-1404.html