I earned a small amount of BTC for a referral on an exchange that I have let sit for a few months. It is under $10US. I wanted to send it to another exchange
Since you already have it in one exchange, you can try to change to an altcoin there.
Since it's an exchange, there's a good chance they pay higher network fee than you should, however, if you afford to wait, then wait. Solutions for faster and cheaper transfer are already in testing phase from what I've read.