...run mycellium so you mine to a cold storage, then use
https://bitinfocharts.com/bitcoin/ mycelium to track your balance)
And then transfer from that adress to the exchange if you must change it to fiat.
What ^he said (that's how I do it, too) - though if you're running mycelium you can see your balance in there at any time. I also don't put in the private key unless I'm about to transfer some coin out, then I put it in just long enough to sign the transaction, and after it goes through I delete the private key.
One MAJOR caveat - don't lose the paper with your (cold) storage address on it...!