You could pick up with just the keycards, but you might throw the tesla delivery person off their script. As
@OCR1 one said, the keys are very easy to delete and add. My recommendation would be to mention nothing about "work phone" to the tesla delivery person, and simply add the tesla app to your work phone (unless your phone is restricted in such a way that you can not install apps on it).
When you replace your personal phone, simply install the tesla app on it, and log in with your tesla account credentials, and pair it with the car as a new key. Once you verify its working, you can delete the work phone from the car.
Also note, that pairing the phone as a key and pairing it for making phone calls / playing music are two different pairings, and just because its paired as one of those does not make it automatically paired for the other (this sometimes confuses new tesla owners).
The only downsides I can see with pairing it on your work phone:
1. Your company might have configured your work phone such that you can not add apps to it from outside of the companies specific app store (possible to do, but in my opinion rare).
2. If the phone is one where they provide the phone and dont use "bring your own device" its likely there is a management client on the phone, and the company can see all the apps on the phone. thus, the company would see the tesla app on the phone (but not the contents of the tesla app). On company phones, the company can usually see the apps on the phone, and remotely manage said phone (unlock, lock, erase). Not that big a deal since you are likely going to drive the car to work anyway.