Yes, as preposters already stated, there are multicoin wallets with integrated exchangers for example on jaxx and coinimi for android. They are safe in my experience, because you own your private keys, but there are aspects, you should be aware.
You must pay at each exchange transfer fees and mostly additional exchange fees.
The leading (only?) exchangers are shapeshift and changelly.
When I use shapeshift, I only exchange cryptocurrency pairs with low transactions fees like Dogecoin and Litecoin.
I used changelly, but wouldn't do that again within Coinomi, because the exchange rates are not shown before exchange button is clicked. There are shown rates, but they can change during transfer, that is proceeded quite long. So I never know, if I am making a good or bad deal. They should change that and take shapeshift's procedure as example.
Shapeshift is far way more better than on changelly since we do have the same thing been searching off like on the rates which cant really be shown on changelly which we can able to see on shapeshift.For some this thing might not important but if you are keen on making deals this would really be needed for you to know.On topic, exchange and solely wallet are entirely different.
