Question... I have an old paper wallet (same age, type, code, etc) that has .0001 BTC on it which is currently equivalent to $10.39, so would I be able to use that as a "sweep test" in Electrum to send it to my friend, or is that amount too low with transaction fees?
You can. That's much more that the fee you have to pay for your transaction.
Your transaction will include 1 legacy input an 1 native segwit output and it will be around 190 vbytes.
Currently, miners are including transactions 1 sat/vbyte in the blockchain. Even if you are in a hurry and use the fee rate of 2 sat/vbyte, you will pay around 380 sat as transaction fee and you can create an output worth around 0.000096 BTC.