SSIS has a deployment utility to help with these sort of things. Right click your project name at the top in BIDS > properties > deployment utility.... set CreateDeploymentUtility = true. Next build the package.

Then inside the project's windows directory, a bin\deployment folder will be created along with a manifest file. Move these contents to the machine you want to deploy your updated package to and follow the wizard prompts after running the manifest file on that machine.