Written by the people building Melmex, from how it actually works.

Every wallet claims to be secure. Far fewer are willing to say what happens when things go wrong, because the honest answer is uncomfortable: with a self-custodial wallet, nobody can help you. That is not a gap in the product. It is the product.
A crypto account on an exchange is not really yours. The exchange holds the keys, records that you are owed a balance, and pays out when you ask. That arrangement has real advantages. You can reset a password, call support, and recover from your own mistakes. It also has one property people discover only at the worst moment: if the exchange freezes, fails, or decides your account looks suspicious, the balance in your account is a claim against a company rather than money in your hand.
Self-custody inverts that. The key that controls your assets is generated on your device and stays there. Melmex never sees it. When you send, swap, or sign anything, the signature happens locally and only the finished transaction reaches the network. There is no account on our side to freeze, because there is no account.
We can show you what you hold, price it, route a swap through the open market, and build a transaction for you to approve. We cannot move your assets, reverse a transfer, recover a lost key, or stop someone who has your key from using it. If a support page ever tells you otherwise, you are not reading about a self-custodial wallet.
The benefit is straightforward: no intermediary can lose, freeze, or lend out what you hold. The cost is equally straightforward: the responsibility that an exchange absorbs is now yours. Most people who lose crypto do not lose it to a dramatic hack. They lose it to a device that died with the only copy of a key, a recovery phrase photographed and synced to a cloud account that was later breached, or a signature given to a page that looked familiar.
Export your key and store it somewhere that survives your device. A written copy in a place you would keep a passport beats any screenshot. Second, read what you are signing: the review screen exists so that nothing leaves your wallet before you have seen the amount, the destination, and the fee. Third, keep large holdings on a hardware wallet and connect it when you need it. Melmex speaks WalletConnect, so a hardware wallet works here like any other.
A wallet that could move your assets would eventually be asked to. Building without that ability is what makes the promise credible: not a policy that we will not touch your funds, but an architecture in which we could not if we tried. The server behind Melmex does not even keep your address. It prices assets and routes quotes, and forgets you between requests.
That is a smaller product than a custodial one, and deliberately so. It does less, and what it does, it does without asking you to trust anyone.