To operate or not to operate?

Just got my cat X-rayed today. He has been vomitting non-stop every single time he eat, and it is not because he eats too fast or have heavy meal. Even one tiny piece of dry nibblets could make him puke like there's no tomorrow. Based on the x-ray results, there is a foreign matter in his tummy. Now the vet hasn't confirmed it yet, but there might be an option to operate, or let my cat to eventually vomit or pass motion the matter out. Operation would be quick, but my cat has been under too much stress, I am unsure whether this is the best option. Any suggestions?