Still most of the crypto wallets has its own exchange where one can do trading or exchange. Crypto wallet is for free to attract its user to use its platform but in the end when moving to another wallet or trading fees will apply.

Be careful with other crypto wallet that offer for free. Some of them has controlled over to it and that you should do research before putting coins in that certain wallet. I think there are good crypto wallets that has already establish and many users comfortable using it. There are recommendations in here and that you can read. There are a lot good crypto wallet.

I used Mycelium crypto wallet with trading and exchange. This is not a paid post but base on my experience and with the use of the crypto wallet. I am completely comfortable to use this crypto wallet.