Do you have the coins on cold storage as offline wallet, or are they on paper wallet?
Because the proper way to use a cold storage is to only sign transactions.

Then you maybe export from the cold storage only the master public key or the relevant addresses to an online computer/wallet, create from there the transaction, get it back to the cold storage (with an USB stick for example), sign it, get it back to online computer and broadcast it.

A possibly clearer explanation is here: https://electrum.readthedocs.io/en/latest/coldstorage.html


If you know how to use properly a cold storage it's safer than the hardware wallet. I always recommend hardware wallets only for every day transactions, while the HODL funds should stay on offline cold storage.
If done properly, like the Electrum example (HD wallet, export only master public key, ..), even change address can be used correctly, so you should be good.

Also keep in mind that there's always testnet if you want to try out this kind of things.