I won't attempt to comment on what is allowed. We moved into a new building in 2009. One of the GOOD decisions we made was to contract with a waste disposal firm to move our chemicals. We could have done this job, given enough time and resources. These guys were in and out in no time. There was no doubt that they knew the chemical compatibilities and were in compliance with all applicable regulations. It was a headache we didn't have to deal with, at a time when there were plenty of other things to be done. I suspect that we were moving more chemicals than you are - at least in terms of diversity. We're a smallish regional university, and have the full range of teaching and research labs. However, you will still have plenty of hazardous materials involved in your move. It just takes breaking one bottle of XYZ-. You should have a firm available to do a lab pack in your area, and perhaps you could negotiate a good cost to include disposal of the things you DON'T want to move at the same time. This cost should come out of the building/construction budget.

My answer might change if the move is REALLY close and you could accomplish this safely with a cart in an hour - no vehicles, no streets to cross, no students around. We had to cross a street, which adds all sorts of complexity to the legal issues.

I'd be happy to give you more details if you're interested.