DB2 Express editions is not free; DB2 Express-C is the free edition.
If you license a paid edition of DB2 its license file will be available for download from the usual source, IBM Passport Advantage. DB2 Express-C license is not available separately, it can only be had by downloading and installing the Express-C package, at which point you might as well just use it for your POC.
To install a license file you'd use the db2licm (license manager) utility by running this as the target instance owner:
db2licm -a <path to license file>
You may want to double-check the demo license agreement though -- it probably says that you must remove the demo installation after its license expiration, which would mean that installing the Express-C license into it, though it might be technically possible, would violate the agreement.