No, but running a node will give you more privacy and security. You should be running a node to contribute to the network regardless of your wallet choices. That being said, if you want a good desktop wallet go with Electrum. If you want a mobile wallet go with BlueWallet. If you want an offline cold storage device, I like Ellipal, but there are tons of great options, just make sure it’s an air-gapped device and you are purchasing it directly from the manufacturer.