Signing marriage license during the ceremony

We really like the idea of signing our marriage license during the ceremony! Has anyone else done this?

We are thinking of putting it after exchanging the rings and right before the breaking of the glass (we’re Jewish) and the pronouncement (so the order would be: rings, signing license, breaking glass, pronouncement). Does this seem like the right place to put it?

Also, we’re struggling to find a way for the officiant to introduce the license-signing part of the ceremony. We’re thinking something like: “will the witnesses please join us for the signing of the marriage license” but we’re not crazy about that wording... any suggestions would be appreciated!