from this image, I will prefer to use a non-exchange wallet at first and then if going to sell the coin, it can be sent from the wallet itself.
I know that it will spend more money or fee on the transaction. But at least, it will be safer enough. Moreover, many exchanges will also probably delay or deny our deposit if it is considered from strange platforms or gambling site (moreover if the funds are quite big). there will be several steps that we should follow to recover or to return our funds.
But, if there are some reputable exchanges that don't mind about this, maybe this can be a way if we are directly going to sell the coin.
I would highly recommend the Exodus wallet. It's a wallet which also has an in-built exchange hence is very useful and doesn't charge very high fees for exchanges and they have desktop and mobile versions.
Any wallet that provides you the private keys is a trusted wallet and this is also the reason why centralized exchanges can never serve as good wallets. Blockchain(.)com's wallet is a good one but it does not accept too many coins.
Sometimes I use gambling sites as wallet for small amounts like if I have money in Bitsler I can send to stake and vice versa.