Is it better to swap directly from cold wallet or nah?

Most of my coins are on a Ledger. I've only ever held, never swapped from cold storage. Now I need to move some to USDT for bills.

I see Ledger Live has built-in swaps but I've read horror stories frozen funds, bad rates, funds taking days. Not trying to deal with that.

I also see people connect their Ledger to MetaMask and use external swap tools. Seems more steps but maybe safer?

For people who actually move funds regularly do you swap directly from cold wallet or move to hot wallet first? What's the actual safest way without turning it into a nightmare? Trying to avoid making a stupid mistake.