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You could use cooked shrimp but I would worry about it getting rubbery that close to the top.
Not sure that it would but personally I would chop up the shrimp and mix it in with the cream cheese.
Sure you can but one thing I would do is chop all your other ingredance in a food processor first and then cut up and add the shrimp and just pulse it a few times to chop up the shrimp alittle more then they would be all over cooked and rubbier.