A bit more to trust but a lot less to type.
Not commenting on GP's point but... No, you don't.
You can prepare your transaction on an online machine, without signing it. With full access to the blockchain, the balance of every address, the "counter" needed so that you tx is legal (in Ethereum's case), which address you want to spend from etc.
Then you transfer that transaction, without using the Internet, to the offline computer and sign it there and transfer the transaction back to the online computer to broadcast it.
The computer preparing the transaction, the one signing the transaction and the one broadcasting it can be three different computers.
You can even do that with an hardware wallet: the hardware wallet does not need to be plugged to a computer that is online. It can be plugged to a computer that is offline.
There are still many issues, even when using airgrapped computers. For example it's possible that a hardware wallet vendor is using non-determinism in "random" parameters chosen to sign transactions to exfiltrate the seed hidden among signed transactions. So even an offline/airgapped computer and a hardware wallet hooked to that offline/airgapped computer wouldn't help.
That's an awful idea. If you're the type of person to worry about being supply-chain-attacked, then targeted supply-chain attacks are far more likely to happen to you than untargeted ones are. Specifically, you are more likely to be supply-chain attacked by an entity who has the power to either compel or blackmail the OEM into giving you a first-party-adulterated device (think: Huawei network switches), than by an entity who's supply-chain-attacking random strangers. This doesn't just include governments, mind you, but also any sufficiently-wide-reaching criminal gang.
Showing up in person to the factory — or to a retail store — means the intelligence operative planted there can recognize you, and give you the "special" device prepared just for you; or the employee can be compelled by certain training (required to be allowed to sell such devices in certain countries) to follow the special instructions that come up when they swipe your credit card.
So what to do? Don't show up in person. Send a one-time proxy buyer to show up in person. And have the proxy buyer pay in cash, or using their own card.
Think what an American diplomat stationed in China would do if they absolutely needed to get e.g. a new smartphone right away. Normally they'd just wait for something like that to be sent over from America via diplomatic courier, specifically to avoid this problem. But if they couldn't — then proxy-buying at retail is the next-best solution.
(Funny enough, this is also the same thing that computer-hardware reviewers have to do to avoid getting a "reviewer special" binning of the hardware. Counterintelligence is oddly generalizable!)
The trusted codebase and set of OEMs seems an order of magnitude larger, and I'm not sure whether the lower likelihood of being specifically targeted as e.g. a crypto user by a supplier can make up for that.