Do you cook cooked Shrimp??

I'm not a big fan of sea food but I do love shrimp cocktail. I put all the veggies needed however I got lazy on the shrimp and bought the 'cooked shrimp' bag. It was frozen so I thawed it in a bowl of warm water. Rinsed it and poured it in the cocktail...I thought to myself later...did i have to cook the cooked shrimp? I overthink and I'm picky when it comes to raw meats. I have to make sure they're cooked thoroughly before me eating it. So is it okay if I only thawed the cooked shrimp and put it in the cocktail? theres no going back now..😏