If you want to send very tiny amounts then lowering the transaction fee is not efficient, as it'll still make up a significant fraction of the transaction. In that case you might want to look at opening a Lightning Network channel to send it from instead, which does handle such small values well.
That wouldn't help OP because he still needs to make an on-chain transaction to open the channel, and a second one to close the channel. Plus the fees he would have to pay to move the coins over the LN network. Using LN, he would be paying two on-chain transactions instead of just one, and he owns $0.03 worth of dust.