As long as you have your multi rating and the flight is operated under Part 91, then yes you can log the time while you were sole manipulator of the controls. The captain, however, cannot log this time as PIC even though he is acting as PIC. Part 61.51(e) covers logging PIC time. For Part 91 flying, a recreational, private, or commercial pilot can log PIC time when he is the sole manipulator of the controls of an aircraft for which he is rated, is the sole occupant of the aircraft, or is acting as PIC when more than one pilot is required by the type certificate or the regulations under which the flight is operated. Since the 402 is a single pilot aircraft, and the reposition flight is Part 91 and only requires one pilot, the captain cannot log the time in which you were flying.
I've never heard of logging flight time as total time and nothing else because you are not rated in the aircraft.
There are a couple things to keep in mind here. First of all, the FAA only requires you to log the flight time necessary to show experience needed for a certificate or rating, and to show compliance with the recency of experience regs. So really you can log flight time however you want as long as you comply with 61.51 when using your time to apply for a certificate or rating or when showing the recency of experience requirements have been met. Another thing to keep in mind is that potential employers will want to look at your logbook, and if they see multi-engine time logged before you have your multi rating they are not going to like that (except for the time logged with a MEI.)
You also want to be careful if you log this time after you have your multi rating. You said you fly right seat in the 402 and it's a cargo operation. Are you employed by the company? The FARs say that only company employees, FAA inspectors, etc. may ride along during 135 cargo operations. So you have to be employed by the company and undergo any drug testing, background checks, or anything else that is required. If you are employed by the company than you're okay.
Even though logging this time is legal, keep in mind that many major airlines, and even some of the regionals, only count the time in which you acted as PIC. So if you apply to an airline like this you'll have to remember to subtract this time. Some 135 companies will hire people with less than the 135 IFR mins and then allow them to log the dead legs in order to build up enough time to be a 135 captain. Airnet Express does this, or used to do this, but I might be wrong. It's certainly possible that a future employer will ask you how you logged this time, but as long as you can explain how you were able to legally log it you should be fine. Sorry for such a long reply, but I hope this helps you out.