I have the pin to login cannot find the passphrase (24 words). I'm wondering if both wallets can be connected via usb at the same time when I transfer from one wallet to another, or if both need to be connected at the same time?
To answer this directly:
As far as I am aware, you would only be able to connect and properly use two Trezor devices at the same through a virtual machine or similar. It's overly complicated for what you need, and probably makes the whole process riskier as you run the risk of mixing up which device is which. The much easier way would be to use two separate computers (do you have an old laptop lying around?), or if not, then you will need to only have one wallet plugged in at a time.
Here's the steps I would take:
When the new wallet arrives, follow the instructions at
https://wiki.trezor.io/User_manual-Setting_up_the_Trezor_device to set it up properly, and back up your 24 word phrase on paper. It might be worth creating two paper back ups, and remember where you store them this time.
Set up a new wallet on the new Trezor for the first coin you want to transfer, for example, bitcoin.
Copy and paste your receiving address in to a text editor.
Double and triple check it is correct. For added peace of mind, you could screenshot your screen with your wallet open and address visible, so you know it can't be changed by clipboard malware.
Unplug your new Trezor, plug in your old one, and open your old bitcoin wallet.
Copy and paste your receiving address from the text editor to your bitcoin wallet.
Double and triple check it hasn't changed, and check it against the screenshot of your address taken from your new wallet.
As a side question that hasn't been touched on yet - are you sure you simply lost your 24 word phrase? If there is any chance it has been stolen, you need to move your coins immediately.