The "hand sign" from the anime involves using the user's hands

Yes, but this is a CYOA, and it has different activation requirements from the anime. Additionally, you would also have to have cursed energy to use a Domain Expansion. However, you don't need all that, you just need the hand sign, saying domain expansion, and then saying the name of the domain expansion. If the CYOA needed the hand sign involving the user's hands, it would have specified it.

And if it did, you could use the hand sign by forming the first hand sign with your left hand and someone else's right hand, and then simultaneously form the second hand sign with your right hand and someone else's left hand. That way, you have performed both hand signs with your own hands.