As the comments attest, no - you cannot.
SQL Server Express only allows access to the Import/Export Wizard (which creates and immediately executes an SSIS package. You cannot persist the package you created nor could you run an existing package).
Running an SSIS package outside of the development environment (BIDS/SSDT) requires that the SQL Server Integration Services Service be installed on the machine.
The only way to get the bits for the SSIS Service is to have a licensed copy of SQL Server (not Express edition). That's going to cost you ~ 8k per core for Standard edition or 21k per core for Enterprise edition.
Do not attempt to copy all the required DLLs and registry keys to the client computers. That will result in them being in violation of licensing with Microsoft and they really like getting their money.