Just to be clear: This is not a recommendation you need to do your own due dilligence.
Happened to stumble across Iron Wallet. They have a maybe unique feature: No ETH for gas required:
Before mentioning it here, I wanted to try it once and it works. Will it work in the future, nobody knows. But for now I can say: I was able to transfer STORJ from one wallet to another with Iron Wallet and paid the transaction fees with STORJ. Yay. 
So use that information any way you like.
Link to Iron Wallet: https://ironwallet.io/