I don't really think it's worth it even if you are using a wallet or a separate website for the staking because you never know what happens. What if you have staked a lot of tokens and the price of that token started crashing all of a sudden? And you can't withdraw the staked funds because the contract doesn't allow you to do so, that is when you will lose all the money you have invested if you are not lucky and the price of the token doesn't recover at all.
I know it doesn't happen with all the tokens and coins but when we talk about altcoins, we all know that there are great risks involved with them, we have seen altcoins crashing to almost zero and leaving all their investors stunned losing thousands of dollars in investments in that single altcoin.
1. You shouldn't stake on a "separate" website. If you use centralized exchange or a service that offers staking, you will be giving up your coins to them. You won't own any of the coins, the rates are going to be shit, the fees will leave you with no profit and the risk is very high.
2. That's the risk associated with staking on your own wallet. You have to lock your coins. So stake only if you are willing to hold long term. If you don't want to lock your coins, as far as I know, there are some coins that you can stake on a pool without having to lock your coins. Try using those coins.