exch.cx is too risky for me, nothing against the operators, but changing such large sums to someone who has control over my coins would give me a lot of stomach ache.
In general I would recommend, regardless of the tool you're finally using, to first try it out with lower amounts you can afford to lose. Even in atomic swaps there may be situations where a party can get an unfair advantage, although stealing the funds if you act correctly is not possible.
Atomic swap sounds interesting.
Is something like that safe?
If carried out correctly and monitored by both parties, an atomic swap is safe, yes. The risk is mainly that one of the parties can abandon the trade if the price evolution doesn't favour it, and the other party may sit on transaction fees.
The "smart contract hacks" list linked by Despairo does not really include hacks of traditional atomic swap platforms. There is an attack on Uniswap listed, but Uniswap is a more complex product with more risks involved, and it only supports Ethereum tokens.
And how does an atomic swap work?
The basic principle is simple: Two parties (Alice - altcoin buyer/Bitcoin seller - and Bob - altcoin seller/Bitcoin buyer) arrange transactions (two on each chain) in a way the funds on them can be used only if a secret (generated by one of the parties) is known by both parties. The exact process is described
here (Tier Nolan is the inventor of the first really usable atomic swap technique).
The process can also be moved offchain to save fees (using Lightning Network), but that needs additional monitoring (you have to stay online until the whole process has concluded) and
can be a little bit less safe.
As far as I know, everything runs with AMM (Automatic Market Maker), and about smart contracts right?
It's a kind of smart contract but written in Bitcoin Script, i.e. without loops, this means it does work very differently from the contracts you may know from Ethereum. Both parties of the trade generate transactions with a set of rules to ensure that the funds moved by their transactions (the Bitcoin transaction and the altcoin transaction) can only be spent by the other party if it follows by the rules, and if not, then the funds can be spent by themselves again after some time has passed. These contracts are called HTLCs (Hashed Time Locked Contracts, similar to those used in Lightning Network). In its raw form, this kind of atomic swap does not not use AMMs.
And you have full control over it yourself?
Yes.
About tools: Despairo has already linked my thread, so go there for a list of tools/platforms. (Edit: Take into account that also Blocknet and Thorchain are on the list of this thread. Both require trust in an additional blockchain, and Thorchain does indeed use a different model which is not totally trustless.)