We know from what BS has said that the Seanchan do not have the ability to create bloodrings. It is certainly possible that they did, and they no longer do, but there is nothing to suggest that. There is nothing really to suggest the shadow was responsible either though, but its an interesting thought.

As for assassins, while it is true that the shadow already had assassins in gray men and such, that does not mean that they would not have been happy to have other ways too. The seanchan find extremely skilled fighters to take on the ring, and they give up their lives willingly "for the empress" by taking and using the rings. However I could see the shadow using the rings via compulsion for example and actually have someone on the side of light suddenly become superhuman warriors that kill as many of their friends and allies as possible.

That kind of atrocity would certainly please the forsaken I would say. It would in some ways be even more effective than gray men, since even if you see the assassin, the knowledge that its someone on your side, maybe even a friend or a relative, would certainly give you pause, and that would likely be fatal since unlike the gray men, the ring does not just make you hard to see, it enchances your abilities too.