Do I need to be with my Inheritance Recipient to share the Mobile Key?

You don't need to be physically together. During set up, you'll be able to share the QR code through the Casa app using any method you prefer, such as email or text message. You just need to be able to show/send them the image of the QR code. This could be a screenshot or shown live on a video call.

Importing a copy of your Mobile Key is only possible for the account owned by the person you invited to your Inheritance setup. There is no danger in sharing the QR code openly. 

Here is how you can access the QR code version of the Mobile Key to share it with the Recipient of your Inheritance.