Thanks for pointing me to that software, will try to test it. A question arises: Would it be possible to use SPV wallets like Electrum for atomic swaps? If yes, then the storage problem would be solved.
I think not, because you are dealing with a complete stranger- perhaps an adversary. So you must validate for yourself that you have e.g. 1 confirmation and you really can't trust any external party for that information. There is also the question of adversarial forks, so this would be the only way to guarantee you are running on the chain you think you are, and that your trading partner is not trying to use a slightly different chain. But I'm sure these services will be made available anyway, and people will use them without thinking about it

If SPV wallets are not possible, Bitcoin 0.11+ style pruning could be the solution for that - a merchant then could easily accept up to about 100 currencies with ~1GB storage use for every chain.
You'd probably only be able to trade with other people who have the same pruning settings on their chains, but this is just a wild guess. The properties of the trading pairs are a key consideration, and would have an impact on your storage requirements. For example, with Monero you don't need to download the blockchain, you can connect to a remote node. So additional storage would not be required if you're swapping XBT/XMR. But a ETH/XBT swap is a totally different story, you'd have to have massive storage for that swap.
I think by their very nature, XCATs are going to be much slower than the centralized services that are available today. I think each swap, at least where Bitcoin is involved, will take at least 10 minutes. I don't really imagine XCATs will be used by "traders/speculators", but rather by people who genuinely wish to exchange 10 XBT for 500 XMR, wishing for complete privacy, near zero cost and assurance that the trade will not fail.