If you are running sp_change_users_login 'Report'
to get that list of orphaned users it will return the SID expected.
Just take that SID and create your login with the same SID:
CREATE LOGIN [mylogin] WITH PASSWORD='', SID = <SID for orphaned user>
This should allow your login to be mapped
to that user in the database and allow you to access the database.
If you want to copy
a login from production to your development box you can query sys.syslogins
to get the SID, or just use sp_help_revlogin
procedure from KB918992.