Option 1: Lock yourself in the server room and refuse to come out until management change their minds.
If that's not feasible, you've got a few problems to consider:
Cabinets: Easily overlooked: Make sure your rack(s) (if you have any) will fit in the new room and through the door (or in the elevator), or factor complete disassembly/reassembly into your time estimate.
Power: Do you have these servers on a separate circuit? Will you need to re-route that power to the new location?
Environment: Do you have separate AirCon for the room? Are you going to be able to route the pipework and ducting for the new location?
PBX: These are usually portable enough. I'm in the UK, so things may vary a little, but it's probably just a matter of getting your provider in to route the incoming lines to the new site from the distribution board. Depending on your service contract, you might have to get them to move the PBX for you, though.
Internet: As with the PBX, you'll need to cooperation of your provider, here. They'll have to come in and move the lines to the new location. Moving service terminations needs the cooperation of the provider, usually. They get upset if you mess with anything before the demarcation point (usually the smartjack/NID/Distribution board).
Structured Cable: If I understand your question, you want to keep the ports you have already and add more to cover the new office space, while moving the whole patch panel to the new location. Consider that you'll probably have to move most of your furniture and disconnect most of the computers during the work. If you have a raised floor, the installers will need to be able to pull most of it up in one go, which is a massive upheaval in an occupied office.
If at all possible, avoid having a split setup with ports terminating in two different locations. It's a pain to manage and, with only 40 ports, it's not a big enough network to necessitate it. Besides, I would assume you need to surrender the existing space entirely, hence the need to relocate? Leaving ports there is likely to be unsecured and ugly, though that depends on your office layout.
Make no mistake, this is going to be a disruptive job. To make it easier, try to get management to sign off getting stuff like AirCon and power installed in advance. Ask your providers if they'll run new terminations up to the new room, first, before switching over on a named date. If the structured cable run can be done over a weekend (~40 ports should be feasible), then enlist the help of the staff in prepping the ground on the Friday afternoon. Get them to ensure they're shutdown and unplugged and maybe even move their own kit to a store room (there'll be breakages, naturally.) and help with the furniture.
I still favour option 1, of course, but good luck. :)