How can I buy and sell my Bitcoin from a Trezor or Ledger hardware wallet, without sending Bitcoin to an exchange? For example, are there any hardware wallets that allow you to keep your Bitcoins on a hardware wallet and buy and sell. This would mitigate the risk of an exchange getting hacked.
Both are quite easily done. Selling and buying bitcoin, straight from a hardware wallet, can be done at the so called 'fiatgateways' such as www.satos.nl (dutch), I believe Changelly deals with the same strategy. You simply open an sellorder and simply send the amount you have set to sell to the walletadres (straight from your ledger) given by the fiatgateway. Buying is exactly the same at these fiatgateways, not an exchange which comes in between your coins. Your keys, your coins! :)
Try hodlhodl.com, which is non-custodial exchange.