For a pull string, borrow an old trick used by telephone guys.
Get a string twice as long as the chase, then mark it in the center with a Sharpie.
Pull the string into the chase, then attach both ends of the string permanently to a nearby screw or other appendage.
Then pull the string to one end, and coil up the remainder. Put it into a zip-lok bag or something similar to protect it.
When you need to pull another wire, uncoil the string, then attach the wire to the black center mark. Then pull the string the other direction. The wire will get pulled through the chase, and the string will now have its excess on the other end, ready to be pulled back or recoiled for storage.
Maybe a bit like flossing, but you get the idea. You'll have a permanent pull string that can be reused many times.