A hot wallet signs on a phone that opens websites every day. A hardware wallet signs on a gadget: the computer shows “send 2 ETH”, the Yes button lives on the device screen.
It is still a non-custodial wallet. The seed appears at setup. You write that on paper too. Lost the device, seed intact — buy a new one, restore. Lost the seed — the device will not save you.
When it is time
Not after the first $30 swap. When the address holds an amount you would hate to donate to phishing. The household split from wallet types: hot for operations, hardware for the rest.
How it meets Uniswap
The companion app on the PC talks to the device. Uniswap asks for a signature — you confirm on the device, reading the address and amount on its screen, not only in the browser.
Do not type a seed into Ledger Live / Trezor Suite “following Discord instructions”. Official apps ask for a seed only during a restore that you started.