+1 on the repair kit.

If you're repairing computers that often, set up a dedicated kit for it. I set one up in a tool box sized tackle box. This is slightly overkill but it was what I could find with the compartments I wanted.

If the company you're going to be doing the repair for will call down to security they will probably grant an exception for an expected repair tech with a tool kit. For a more suit & tie environment I'd have looked harder at modifying one of the aluminum briefcases or something like this or this. Before you go in transfer the sharps to the tool kit.