You should go through the chain of command. All TA units (including CVHQs) hold a pool of No 2 dress uniforms. There should be no issues with you drawing a uniform for that especially if the invitation says uniform and medals should be worn by service people.. However before the Q man will issue it to you he will probably want authorisation, which is why you need to go through the chain of command.
BTB don't be put off if the first person you ask says no - ask to speak to the next one up - and don't stop until you get to at least OC level. The reason I mention that is because all to often the person you ask will say no because your request might involve them in doing something and its easier to say no than bother to do their jobs properly.
PS. Remember that if you are going to wear No2 at a passing out parade a very high standard of turnout will be necessary. If you are not familiar with wearing No2 find some one who is and who will make sure you are up to scratch. Otherwise you will be letting your brother down and the rest of the TA.