You’re in luck in using a Trezor, which actually makes this somewhat manageable.
The functionality you’re looking for is called Coin Control – where you can specify which existing UTXOs to spend from, hence controlling the address the funds originate from in your deposit transaction to Gemini.
You would have to have enough BTC in some address to be able to first send it to the address you wish to prove ownership of.
Then, you can use the coin control features in Trezor Suite, or connect your Trezor to other wallets that offer similar functionality – Electrum, for example.
