We do not even know certainly if Satoshi still owns any Bitcoin, if any of the old high-balance BTC addresses were/are his .. or if he's even alive anymore. but the best guess would be that Satoshi has used Bitcoin Core.
There are lots of options out there and your question is very nice in my opinion. Well done for looking for wallets without any third parties involved!
My personal suggestions are: Electrum for PC, Mycelium/Electrum for Mobile or, the best one of all, Hardware Wallets (I personally have a Ledger).
There is no safe wallet out there if you do not use them the right way though. Although hardware wallets made me feel the safest, they aren't if you do not take care of the basic but crucial steps such as paying attention to the transaction details, making sure the shown address is correct etc.
By "offline" usage I believe you are talking about airgapping a computer/phone in order to complete transactions on it completely offline. Again, this is NOT a no-risk zone. Don't you think that by airgapping a PC you'd be 100% safe!
If you would like to use an airgapped PC, you could go for Electrum.
Here is a very quick tutorial on how to set up your Electrum wallet for this matter.
If you are quite new to Bitcoin, which I assume you are, I highly recommend you to first transfer $5-10 to the wallet and test all wallet functions out to avoid large losses. Once you get used to the wallet, go ahead and store your little pieces of the Crypto King in it. One more friendly advice: don't give
anyone your master seed/mnemonic phrase/private key(s) and better triple-check an address or the details of a transaction than be sorry. You might waste a minute on checking if the transaction details are correct, but maybe you're going to prevent the loss of significant amounts.