You can transfer that Bitcoin without using a fee. There are several methods and they include time, collateral money or both:
- Send it with 0 fee and wait 4-40 hours until it is prioritized high enough and some pool or miner agrees to accept it
- Send to yourself or the destination only some of the inputs such that the fee is 0, repeat until you spend it all
- Send to yourself the inputs grouped in such a way that the fee is 0, wait a few hours until the spent coins can be merged again and repeat until you spend it all
- Send the inputs along with a bigger sum of dormant Bitcoin (something like 1+ BTC) and ferry the inputs one by one grouped with this bigger lump until you merge them all
- Ask a miner nicely to include your transaction without a fee and send it to him
I am eager to wait for your reply as to the method used to spend nothing to send that 1 Bitcoin, while wasting several hours of your precious time that apparently is less than 1$/hour