If it’s a whole shrimp it might take longer than a week to truly break down. If it’s the sort of shrimp you’d use for food it’s pretty big. Hence why cycling that way versus putting liquid amonia in the tank takes longer. I cycled my 40b with dr Tim’s (which is readily available on brs) took me a week and a half. You are likely still going to get your cycle done. You just need to take into account the time for the whole shrimp to rot.
I guess I’d put it like this. I put a clam on a half shell in the tank I’ve got running now. I have some marine pure balls and the bio media that comes with my hob filter cycled. It’s not super robust bio filtration; I don’t have a skimmer. But from what I’ve observed with my paranoid over testing of nitrates, two days of leaving It in doesn’t result in a noticeable spike in nitrates or nitrites. And I have a valentini (very messy eater) in the tank along with 4 other fish in growing out for my DT, and a bunch of hermits. Yes my tank is cycled. But if such a comparably small amount of organic matter doesn’t immediately break down in the rotting process, a large shrimp will take more time.
From what I’ve read, using the rotting shrimp method is indeed better than sacrificing a fish, but it’s still not nearly as fast of a cycle as skipping straight to the ammonia. I’m by no means an expert at all, but as I was overly worried about cycling my tank with dr Tim’s ammonia and it still took a week... I can only imagine that you’d need to allow more time for the shrimp to go through the decaying process. Everything I read before deciding to just use straight AC indicated that the ghost feeding and shrimp method would take longer, because you’re not only waiting for your bio filtration population to grow; you’re also waiting for the organic matter to break down to the point where it is really providing enough for the bacteria to go to work.
Thus, in my limited experience, I’d say just give it a bit more time. The cycle is going to happen as long as you have a viable culture of bacteria added. A week is pretty quick for the organic matter to rot enough.