Copying an old private key (from 2011) into Electrum: any risks? I have an old phone, with a version of the Bitcoin wallet from 2011.  It has a few satoshis in it, which are now worth enough to be worth recovering.  However, the phone can't connect to the Internet.

This version of the wallet apparently stores the private key in an unencrypted base58 file, which I think is therefore equivalent to the Wallet Import Format.  I have root access, so I can view any file on the system, so getting it out isn't a problem.

Would there be any risks involved in simply copying the private key into Electrum 3.0 using these instructions and then sending the contents to a more modern wallet?  

From my understanding, the private key gives full access to the contents of the address, but a friend told me that given the key's age, I'd need to import it into bitcoin-qt and do a full sync in order to make sure that the address works properly.
No, Bitcoin Core (formerly known as Bitcoin-QT) is not a wallet, it is a full node software + wallet, so there are better software to use as a wallet. Sure, you can use Bitcoin Core, but you'll need to keep your Bitcoin Core connected to the internet for days to synchronize.

To summarize, you should use a wallet software (sure, Electrum!) to import (or sweep the funds of) the private key.

Note: A few satoshis is worthless. The median transaction fee is currently 110,740 satoshis. according to this.