$40 for transaction

Hi! I have bought a Trezor for my gf and we were about to send her btc to it but then I realized that the transaction costs 1/5 of her stack. I haven’t really noticed it before as the sums I was sending to my cold wallets were way bigger, but in her case it seems like a huge waste of money, especially that you should always make a test transaction first.. 2/5 of the stack? No thanks.

Is there a way to send it offchain instead of onchain to the coldwallet? I Offchain tnx costs around 1 usd.. I checked both segwit and native segwit, same price of 0,0006 btc which is around $40.

Appreciate the answers! Have a great day ????