I've been using Exodus, and have my daily cloud mining payments go there.
I have about $18 worth of BTC that has built up from daily payments.
But when I go to send or exchange with the wallet, my fee is close to $16
This is not the case with my DASH daily payments, this is a BTC only situation.
Here is the response from Exodus support:
If you type a small amount into the amount box it will show you the fee you have to pay to send BTC on the bottom right edge of the popup.
If you have a number of small payments over time from a mining contract when you finally send these out as one payout the Bitcoin network requires these inputs be put together and batched into one payment. The fees on these transactions are typically more than just sending a regular transaction.
Long story short, if you have a bunch of small inputs and have to combine those into one larger input this is more work on the Bitcoin network and requires a larger fee to process this transaction. This is similar to taking a large jar of change and counting it up, adding it all together then converting it into large bills and sending it on. I have seen fees as high as $10 - $70 for mining contract payouts that have gone on for years.
If you can get larger payments from your mining contract vs. daily small payments that will also help.
Here is more info on how Bitcoin transaction fees work:
https://en.bitcoin.it/wiki/Transaction_fees