Best way to minimise ETH transfer fees with hard wallet?

I want to move my ETH from Kraken to a hard wallet (I've got Ledger and Keystone) and it costs 0.003 ETH to move it on the ETH chain, but only 0.00015 ETH on Arb Nova, Arb One, Optimism or Polygon.

I do need to have some ETH on the ETH chain, like $100, to pay for gas fees as I don't think they can be paid with ETH on the other chains.

Would the best option be to withdraw $100 on the ETH chain and pay the 0.003 ETH fee, then withdraw the rest on one of the other chains and pay the 0.00015 ETH fee, so when I want to move it back to a CEX to sell in future I only have to pay the low fee?

Are any of those chains better/safer than the others? Are they all supported by Ledger and Keystone?