Services may promise you a lot, but it's better to use what has been proven to work. Take VPN providers as an example: how many have said they don't log anything, but in the end the police were still able to identify the user (e.g. NordVPN)? That's why you should use proven services such as Mullvad or Perfect Privacy.
But this is about anonymizing cryptocurrency, so forget about those swappers that promise you anonymity and use the technology that has been proven to work: Monero.
If you are familiar with blockchain, you know that there are companies that analyze it and have already exposed several hacks that were not known. The police will certainly have at least the same resources︀ or will be able to call on these companies.
It should be a lesson to︁ you that in the past 12 months, a great many mixers have been busted.